task_id stringlengths 23 52 | subset stringclasses 1
value | family stringclasses 80
values | problem_key stringclasses 75
values | domain stringclasses 8
values | tier stringclasses 2
values | level stringclasses 6
values | source stringclasses 80
values | license stringclasses 3
values | tags listlengths 0 4 | prompt stringlengths 308 37k | instance stringlengths 56 37.8k | direction null | baseline null | best_known null | reference_answer stringlengths 8 198k | reference_reward float64 1 1 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
construct-ae-p32-spherical-design-l1-s0 | construct | ae_p32_spherical_designs | spherical_t_design_s2 | discrete_geometry | research | 1 | AlphaEvolve-Repository-of-Problems/32-spherical-designs | CC-BY-4.0 | [
"float_tolerance",
"numerical_design"
] | Spherical designs on the 2-sphere.
A finite set X of points on the unit sphere S^2 in R^3 is a spherical t-design if for every polynomial P(x, y, z)
of degree at most t, the average of P over the points of X equals the average of P over the whole sphere
(with respect to the uniform surface measure). Equivalently, the... | {"t": 7, "N": 32, "family": "ae_p32_spherical_designs", "subset": "construct"} | null | null | null | {"points": [[0.11606245518956762, -0.16610236292160294, 0.9792545693164928], [-0.39675347898353364, 0.021959702877615433, 0.9176624915316032], [0.48607965266991554, 0.3267742455138338, 0.8105215381031888], [-0.5028561752354322, -0.5750524338141748, 0.6453296563710569], [-0.028977008371302036, 0.6135860519291835, 0.7890... | 1 |
construct-ae-p32-spherical-design-l2-s0 | construct | ae_p32_spherical_designs | spherical_t_design_s2 | discrete_geometry | research | 2 | AlphaEvolve-Repository-of-Problems/32-spherical-designs | CC-BY-4.0 | [
"float_tolerance",
"numerical_design"
] | Spherical designs on the 2-sphere.
A finite set X of points on the unit sphere S^2 in R^3 is a spherical t-design if for every polynomial P(x, y, z)
of degree at most t, the average of P over the points of X equals the average of P over the whole sphere
(with respect to the uniform surface measure). Equivalently, the... | {"t": 9, "N": 50, "family": "ae_p32_spherical_designs", "subset": "construct"} | null | null | null | {"points": [[0.16922693235862724, -0.20103306308114954, 0.9648564416081281], [-0.1444229652425299, 0.2171017544618927, 0.9654060468632476], [0.43300572300753354, 0.1842363624211028, 0.8823621742825126], [-0.19147178208270688, -0.49237023697924936, 0.8490642534008073], [-0.22349668833015543, 0.654913436090283, 0.7218986... | 1 |
construct-ae-p32-spherical-design-l3-s0 | construct | ae_p32_spherical_designs | spherical_t_design_s2 | discrete_geometry | research | 3 | AlphaEvolve-Repository-of-Problems/32-spherical-designs | CC-BY-4.0 | [
"float_tolerance",
"numerical_design"
] | Spherical designs on the 2-sphere.
A finite set X of points on the unit sphere S^2 in R^3 is a spherical t-design if for every polynomial P(x, y, z)
of degree at most t, the average of P over the points of X equals the average of P over the whole sphere
(with respect to the uniform surface measure). Equivalently, the... | {"t": 11, "N": 74, "family": "ae_p32_spherical_designs", "subset": "construct"} | null | null | null | {"points": [[0.012181667145405233, 0.04406897535978663, 0.9989542193695851], [-0.34509997965572176, 0.1288545422759548, 0.9296787138449899], [0.23747361043298654, 0.3418894723530763, 0.9092402724484091], [-0.32378205632304635, -0.3291285139317033, 0.8870397969202556], [-0.10993350849569812, 0.5729830527072197, 0.812160... | 1 |
construct-ae-p32-spherical-design-l4-s0 | construct | ae_p32_spherical_designs | spherical_t_design_s2 | discrete_geometry | research | 4 | AlphaEvolve-Repository-of-Problems/32-spherical-designs | CC-BY-4.0 | [
"float_tolerance",
"numerical_design"
] | Spherical designs on the 2-sphere.
A finite set X of points on the unit sphere S^2 in R^3 is a spherical t-design if for every polynomial P(x, y, z)
of degree at most t, the average of P over the points of X equals the average of P over the whole sphere
(with respect to the uniform surface measure). Equivalently, the... | {"t": 15, "N": 120, "family": "ae_p32_spherical_designs", "subset": "construct"} | null | null | null | {"points": [[-0.6797362419565781, -0.33277023955514695, 0.6536226809384437], [0.9801860827417008, 0.15541248185198572, -0.12280962374376724], [-0.3823571350063186, 0.8762371708640566, -0.2932770732701655], [0.3500260050652461, 0.4693794053767845, -0.810656998727699], [-0.9252524215421856, 0.31148183475383806, -0.216534... | 1 |
construct-ae-p32-spherical-design-l5-s0 | construct | ae_p32_spherical_designs | spherical_t_design_s2 | discrete_geometry | research | 5 | AlphaEvolve-Repository-of-Problems/32-spherical-designs | CC-BY-4.0 | [
"float_tolerance",
"numerical_design"
] | Spherical designs on the 2-sphere.
A finite set X of points on the unit sphere S^2 in R^3 is a spherical t-design if for every polynomial P(x, y, z)
of degree at most t, the average of P over the points of X equals the average of P over the whole sphere
(with respect to the uniform surface measure). Equivalently, the... | {"t": 19, "N": 198, "family": "ae_p32_spherical_designs", "subset": "construct"} | null | null | null | {"points": [[0.2527759326534977, -0.9566791840084274, -0.14446199069694396], [-0.9071773294756267, 0.015962244615743904, 0.4204455965190948], [-0.616471714044581, -0.20797033654468083, -0.7594148832492214], [-0.6669229800600651, 0.5278085911769907, 0.5259580113921283], [-0.6636953921393339, 0.3035315017983519, 0.683649... | 1 |
construct-ae-p32-spherical-design-l6-s0 | construct | ae_p32_spherical_designs | spherical_t_design_s2 | discrete_geometry | research | 6 | AlphaEvolve-Repository-of-Problems/32-spherical-designs | CC-BY-4.0 | [
"float_tolerance",
"numerical_design"
] | Spherical designs on the 2-sphere.
A finite set X of points on the unit sphere S^2 in R^3 is a spherical t-design if for every polynomial P(x, y, z)
of degree at most t, the average of P over the points of X equals the average of P over the whole sphere
(with respect to the uniform surface measure). Equivalently, the... | {"t": 21, "N": 234, "family": "ae_p32_spherical_designs", "subset": "construct"} | null | null | null | {"points": [[-0.9596810424419001, -0.28105208802161075, 0.0046926108213612315], [-0.7595309788778035, 0.28634046819989534, -0.5840563572087804], [-0.813730818738408, -0.3764390859035123, 0.4428721816048601], [-0.9347893044111631, 0.08032069257362744, 0.34600222933239383], [-0.2683002097771996, 0.8777526186055353, -0.39... | 1 |
construct-ae-p38-factorial-factors-l1-s0 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 1 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 36. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 10. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your numbe... | {"N": 36, "t": 10, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [60, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 17, 17, 19, 23, 29, 31]} | 1 |
construct-ae-p38-factorial-factors-l1-s1 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 1 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 37. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 10. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your numbe... | {"N": 37, "t": 10, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [60, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 17, 17, 19, 23, 29, 31, 37]} | 1 |
construct-ae-p38-factorial-factors-l1-s2 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 1 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 44. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 12. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your numbe... | {"N": 44, "t": 12, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [96, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 17, 17, 19, 19, 22, 22, 22, 22, 23, 29, 31, 37, 41, 43]} | 1 |
construct-ae-p38-factorial-factors-l1-s3 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 1 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 45. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 12. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your numbe... | {"N": 45, "t": 12, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [24, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 17, 17, 19, 19, 22, 22, 22, 22, 23, 29, 31, 37, 41, 516]} | 1 |
construct-ae-p38-factorial-factors-l1-s4 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 1 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 48. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 13. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your numbe... | {"N": 48, "t": 13, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [52, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 18, 18, 18, 18, 18, 18, 19, 19, 22, 22, 22, 22, 23, 23, 29, 31, 37, 41, 43, 47]} | 1 |
construct-ae-p38-factorial-factors-l1-s5 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 1 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 52. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 15. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your numbe... | {"N": 52, "t": 15, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [45, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 18, 19, 19, 21, 21, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 23, 23, 26, 26, 26, 26, 29, 31, 37, 41, 43, 47]} | 1 |
construct-ae-p38-factorial-factors-l1-s6 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 1 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 54. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 15. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your numbe... | {"N": 54, "t": 15, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [120, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 18, 18, 18, 19, 19, 21, 21, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 23, 23, 26, 26, 26, 26, 29, 31, 37, 41, 43, 47, 53]} | 1 |
construct-ae-p38-factorial-factors-l1-s7 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 1 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 55. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 15. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your numbe... | {"N": 55, "t": 15, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 18, 18, 19, 19, 21, 21, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 23, 23, 26, 26, 26, 26, 29, 31, 33, 37, 41, 43, 47, 795]} | 1 |
construct-ae-p38-factorial-factors-l1-s8 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 1 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 56. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 15. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your numbe... | {"N": 56, "t": 15, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [60, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 18, 18, 19, 19, 21, 21, 21, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 23, 23, 26, 26, 26, 26, 29, 31, 37, 41, 43, 47, 795]} | 1 |
construct-ae-p38-factorial-factors-l1-s9 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 1 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 59. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 17. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your numbe... | {"N": 59, "t": 17, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 23, 23, 24, 24, 24, 24, 26, 26, 26, 26, 29, 29, 31, 37, 41, 43, 47, 53, 59]} | 1 |
construct-ae-p38-factorial-factors-l2-s0 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 2 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 86. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 24. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your numbe... | {"N": 86, "t": 24, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [288, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 27, 27, 27, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 29, 29, 31, 31, 33, 33, 33, 33, 33, 33, 33, 34, 34, 34, 34, 34, 37, 37, 38, 38, 38, 38, 41, 41, 43, 43, 46, 46, 46... | 1 |
construct-ae-p38-factorial-factors-l2-s1 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 2 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 88. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 25. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your numbe... | {"N": 88, "t": 25, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [150, 25, 25, 25, 25, 25, 25, 25, 25, 25, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 29, 29, 29, 31, 31, 32, 32, 32, 32, 32, 32, 32, 32, 33, 33, 33, 33, 33, 33, 33, 33, 34, 34, 34, 34, 34, 37, 37, 38, 38, 38, 38, 41, 41, 43, 43, 46... | 1 |
construct-ae-p38-factorial-factors-l2-s2 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 2 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 97. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 28. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your numbe... | {"N": 97, "t": 28, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [336, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 29, 29, 29, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 31, 31, 31, 32, 32, 32, 32, 33, 33, 33, 33, 33, 33, 33, 33, 34, 34, 34, 34, 34, 36, 36, 36, 36, 37, 37, 38, 38, 38, 38, 38, 39, 39, 39, 39, 39, 39, 39... | 1 |
construct-ae-p38-factorial-factors-l2-s3 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 2 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 106. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 30. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your numb... | {"N": 106, "t": 30, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [360, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 31, 31, 31, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 33, 33, 33, 33, 33, 33, 33, 33, 33, 34, 34, 34, 34, 34, 34, 36, 36, 36, 37, 37, 38, 38, 38, 38, 38, 39, 39, 39, 39, 39, 39, 39, 39, 41, 41, 42, 43, 43, 46... | 1 |
construct-ae-p38-factorial-factors-l2-s4 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 2 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 110. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 31. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your numb... | {"N": 110, "t": 31, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [186, 31, 31, 32, 32, 32, 32, 32, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 34, 34, 34, 34, 34, 34, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 37, 37, 38, 38, 38, 38, 38, 39, 39, 39, 39, 39, 39, 39, 39, 40, 40, 40, 40... | 1 |
construct-ae-p38-factorial-factors-l2-s5 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 2 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 119. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 35. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your numb... | {"N": 119, "t": 35, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 37, 37, 37, 38, 38, 38, 38, 38, 38, 39, 39, 39, 39, 39, 39, 39, 39, 39, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 41, 41, 43, 43, 44, 44, 44, 44, 44, 44, 44, 44,... | 1 |
construct-ae-p38-factorial-factors-l2-s6 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 2 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 120. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 35. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your numb... | {"N": 120, "t": 35, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [245, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 37, 37, 37, 38, 38, 38, 38, 38, 38, 39, 39, 39, 39, 39, 39, 39, 39, 39, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 41, 41, 43, 43, 44, 44, 44, 44, 44, 44... | 1 |
construct-ae-p38-factorial-factors-l2-s7 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 2 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 134. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 39. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your numb... | {"N": 134, "t": 39, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [585, 39, 39, 39, 39, 39, 39, 39, 39, 39, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 41, 41, 41, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 43, 43, 43, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 45, 45, 45, 45, 45, 45... | 1 |
construct-ae-p38-factorial-factors-l2-s8 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 2 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 139. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 40. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your numb... | {"N": 139, "t": 40, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 41, 41, 41, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 43, 43, 43, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 46, 46, 46, 46, 46, 46, 47, 47, 48, 49, 49, 49, 49, 49,... | 1 |
construct-ae-p38-factorial-factors-l2-s9 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 2 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 152. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 44. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your numb... | {"N": 152, "t": 44, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [704, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 46, 46, 46, 46, 46, 46, 47, 47, 47, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 50, 50, 50, 50, 50, 50, 50... | 1 |
construct-ae-p38-factorial-factors-l3-s0 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 3 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 180. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 54. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your numb... | {"N": 180, "t": 54, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 57, 57, 57, 57, 57, 57, 57, 57, 57, 58, 58,... | 1 |
construct-ae-p38-factorial-factors-l3-s1 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 3 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 231. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 69. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your numb... | {"N": 231, "t": 69, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 71, 71, 71, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 73, 73, 73, 74, 74, 74, 74, 74, 74, 75, 75, 75, 75, 75, 75, 75, 75, 75, 76,... | 1 |
construct-ae-p38-factorial-factors-l3-s2 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 3 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 252. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 75. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your numb... | {"N": 252, "t": 75, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [750, 75, 75, 75, 75, 75, 75, 75, 75, 75, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 79, 79, 79, 80, 80, 80, 80, 80, 80, 80... | 1 |
construct-ae-p38-factorial-factors-l3-s3 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 3 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 275. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 83. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your numb... | {"N": 275, "t": 83, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [83, 83, 83, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 86, 86, 86, 86, 86, 86, 87, 87, 87, 87, 87, 87, 87, 87, 87, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88,... | 1 |
construct-ae-p38-factorial-factors-l3-s4 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 3 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 284. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 85. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your numb... | {"N": 284, "t": 85, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 86, 86, 86, 86, 86, 86, 87, 87, 87, 87, 87, 87, 87, 87, 87, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 89, 89, 89, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90,... | 1 |
construct-ae-p38-factorial-factors-l3-s5 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 3 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 313. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 93. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your numb... | {"N": 313, "t": 93, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [930, 93, 93, 93, 93, 93, 93, 93, 93, 93, 94, 94, 94, 94, 94, 94, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 97, 97, 97, 98, 98, 98, 98, 98, 98, 98, 98, 98, 98, 98, 98, 98, 98, 98, 98, 98, 98, 98, 98... | 1 |
construct-ae-p38-factorial-factors-l3-s6 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 3 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 339. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 103. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your num... | {"N": 339, "t": 103, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [103, 103, 103, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 105, 105, 105, 105, 105, 105, 105, 105, 105, 105, 105, 105, 105, 105, 105, 105, 105, 105, 105, 105, 105, 105, 105, 105, 105, 105, 105, 105, 105, 105, 10... | 1 |
construct-ae-p38-factorial-factors-l3-s7 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 3 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 357. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 108. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your num... | {"N": 357, "t": 108, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [972, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 109, 109, 109, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 111, 111, 111, 111, 111, 111, 11... | 1 |
construct-ae-p38-factorial-factors-l3-s8 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 3 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 384. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 117. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your num... | {"N": 384, "t": 117, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 118, 118, 118, 118, 118, 118, 119, 119, 119, 119, 119, 119, 119, 119, 119, 119, 119, 119, 119, 119, 119, 119, 119, 119, 119, 119, 119, 119, 119, 120, 12... | 1 |
construct-ae-p38-factorial-factors-l3-s9 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 3 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 395. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 120. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your num... | {"N": 395, "t": 120, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 12... | 1 |
construct-ae-p38-factorial-factors-l4-s0 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 4 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 568. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 174. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your num... | {"N": 568, "t": 174, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [348, 174, 174, 174, 174, 174, 174, 174, 174, 174, 174, 174, 174, 174, 174, 174, 174, 174, 174, 175, 175, 175, 175, 175, 175, 175, 175, 175, 175, 175, 175, 175, 175, 176, 176, 176, 176, 176, 176, 176, 176, 176, 176, 176, 176, 176, 176, 176, 176, 176, 176, 176, 176, 176, 176, 177, 177, 177, 177, 177, 177, 17... | 1 |
construct-ae-p38-factorial-factors-l4-s1 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 4 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 577. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 178. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your num... | {"N": 577, "t": 178, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [178, 178, 178, 178, 178, 178, 179, 179, 179, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 18... | 1 |
construct-ae-p38-factorial-factors-l4-s2 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 4 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 584. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 180. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your num... | {"N": 584, "t": 180, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [2880, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 1... | 1 |
construct-ae-p38-factorial-factors-l4-s3 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 4 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 736. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 228. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your num... | {"N": 736, "t": 228, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 229, 229, 229, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 23... | 1 |
construct-ae-p38-factorial-factors-l4-s4 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 4 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 751. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 232. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your num... | {"N": 751, "t": 232, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 233, 233, 233, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 23... | 1 |
construct-ae-p38-factorial-factors-l4-s5 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 4 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 778. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 240. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your num... | {"N": 778, "t": 240, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [480, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 241, 241, 241, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 24... | 1 |
construct-ae-p38-factorial-factors-l4-s6 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 4 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 891. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 278. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your num... | {"N": 891, "t": 278, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [278, 278, 278, 278, 278, 278, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 28... | 1 |
construct-ae-p38-factorial-factors-l4-s7 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 4 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 1031. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 322. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your nu... | {"N": 1031, "t": 322, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [2254, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 322, 323, 323, 323, 323, 323, 323, 323, 323, 323, 323, 323, 323, 323, 323, 323, 323, 3... | 1 |
construct-ae-p38-factorial-factors-l4-s8 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 4 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 1117. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 350. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your nu... | {"N": 1117, "t": 350, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 35... | 1 |
construct-ae-p38-factorial-factors-l4-s9 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 4 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 1164. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 365. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your nu... | {"N": 1164, "t": 365, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [365, 365, 365, 365, 365, 365, 365, 365, 365, 365, 365, 365, 365, 365, 365, 366, 366, 366, 366, 366, 366, 366, 366, 366, 366, 366, 366, 366, 366, 366, 366, 366, 366, 366, 367, 367, 367, 368, 368, 368, 368, 368, 368, 368, 368, 368, 368, 368, 368, 368, 368, 368, 368, 368, 368, 368, 368, 368, 368, 368, 368, 36... | 1 |
construct-ae-p38-factorial-factors-l5-s0 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 5 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 1632. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 515. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your nu... | {"N": 1632, "t": 515, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [515, 515, 515, 515, 515, 515, 515, 515, 515, 515, 515, 515, 515, 515, 515, 516, 516, 516, 516, 516, 516, 516, 516, 516, 516, 516, 516, 516, 516, 516, 516, 516, 516, 516, 516, 516, 516, 516, 516, 516, 516, 516, 516, 516, 516, 516, 516, 516, 516, 516, 516, 516, 517, 517, 517, 517, 517, 517, 517, 517, 517, 51... | 1 |
construct-ae-p38-factorial-factors-l5-s1 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 5 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 1725. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 546. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your nu... | {"N": 1725, "t": 546, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 54... | 1 |
construct-ae-p38-factorial-factors-l5-s2 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 5 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 1825. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 577. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your nu... | {"N": 1825, "t": 577, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [577, 577, 577, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 579, 579, 57... | 1 |
construct-ae-p38-factorial-factors-l5-s3 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 5 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 1893. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 599. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your nu... | {"N": 1893, "t": 599, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [1797, 599, 599, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 601, 601, 601, 602, 602, 602, 602, 602, 602, 602, 6... | 1 |
construct-ae-p38-factorial-factors-l5-s4 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 5 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 2295. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 732. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your nu... | {"N": 2295, "t": 732, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [1464, 732, 732, 732, 732, 732, 732, 732, 732, 732, 732, 732, 732, 732, 732, 732, 732, 732, 732, 732, 732, 732, 732, 732, 732, 732, 732, 732, 732, 732, 732, 732, 732, 732, 732, 732, 732, 733, 733, 733, 734, 734, 734, 734, 734, 734, 735, 735, 735, 735, 735, 735, 735, 735, 735, 735, 735, 735, 735, 735, 735, 7... | 1 |
construct-ae-p38-factorial-factors-l5-s5 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 5 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 2400. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 764. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your nu... | {"N": 2400, "t": 764, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [764, 764, 764, 764, 764, 764, 764, 764, 764, 764, 764, 764, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 765, 76... | 1 |
construct-ae-p38-factorial-factors-l5-s6 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 5 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 2989. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 956. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your nu... | {"N": 2989, "t": 956, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [2868, 956, 956, 956, 956, 956, 956, 956, 956, 956, 956, 956, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 9... | 1 |
construct-ae-p38-factorial-factors-l5-s7 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 5 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 3059. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 980. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your nu... | {"N": 3059, "t": 980, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [9800, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 9... | 1 |
construct-ae-p38-factorial-factors-l5-s8 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 5 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 3148. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 1010. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your n... | {"N": 3148, "t": 1010, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [2020, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1011, 1011, 1011, 1011, 1011, 1011, 1011, 1011, 1011, 1012, 1012, 1012, 1012, 1012, 1012, 1012, 1012, 1012, 1012, 1012, 1... | 1 |
construct-ae-p38-factorial-factors-l5-s9 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 5 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 3574. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 1147. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your n... | {"N": 3574, "t": 1147, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [2294, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1... | 1 |
construct-ae-p38-factorial-factors-l6-s0 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 6 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 5043. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 1631. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your n... | {"N": 5043, "t": 1631, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [4893, 1631, 1631, 1631, 1631, 1631, 1631, 1631, 1631, 1631, 1631, 1631, 1631, 1631, 1631, 1631, 1631, 1631, 1631, 1631, 1631, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1... | 1 |
construct-ae-p38-factorial-factors-l6-s1 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 6 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 5728. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 1856. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your n... | {"N": 5728, "t": 1856, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1... | 1 |
construct-ae-p38-factorial-factors-l6-s2 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 6 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 6230. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 2021. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your n... | {"N": 6230, "t": 2021, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [94987, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, ... | 1 |
construct-ae-p38-factorial-factors-l6-s3 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 6 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 7370. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 2398. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your n... | {"N": 7370, "t": 2398, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [28776, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, 2398, ... | 1 |
construct-ae-p38-factorial-factors-l6-s4 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 6 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 7446. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 2426. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your n... | {"N": 7446, "t": 2426, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [9704, 2426, 2426, 2426, 2426, 2426, 2427, 2427, 2427, 2427, 2427, 2427, 2427, 2427, 2427, 2428, 2428, 2428, 2428, 2428, 2428, 2428, 2428, 2428, 2428, 2428, 2428, 2429, 2429, 2429, 2429, 2429, 2429, 2429, 2429, 2429, 2429, 2429, 2429, 2429, 2429, 2429, 2429, 2429, 2429, 2429, 2429, 2429, 2430, 2430, 2430, 2... | 1 |
construct-ae-p38-factorial-factors-l6-s5 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 6 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 7712. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 2510. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your n... | {"N": 7712, "t": 2510, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [22590, 2510, 2510, 2510, 2510, 2510, 2510, 2510, 2510, 2510, 2510, 2510, 2510, 2510, 2510, 2510, 2510, 2510, 2510, 2510, 2510, 2510, 2510, 2510, 2510, 2510, 2510, 2510, 2510, 2510, 2511, 2511, 2511, 2511, 2511, 2511, 2511, 2511, 2511, 2511, 2511, 2511, 2511, 2511, 2511, 2511, 2511, 2511, 2511, 2511, 2511, ... | 1 |
construct-ae-p38-factorial-factors-l6-s6 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 6 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 8484. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 2770. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your n... | {"N": 8484, "t": 2770, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [33240, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, ... | 1 |
construct-ae-p38-factorial-factors-l6-s7 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 6 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 8731. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 2851. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your n... | {"N": 8731, "t": 2851, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [14255, 2851, 2851, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, ... | 1 |
construct-ae-p38-factorial-factors-l6-s8 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 6 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 8823. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 2881. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your n... | {"N": 8823, "t": 2881, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [69144, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, ... | 1 |
construct-ae-p38-factorial-factors-l6-s9 | construct | ae_p38_factorial_factors | factorial_into_n_large_factors_A034258 | number_theory | research | 6 | AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial | CC-BY-4.0 | [
"agentic_trivial",
"exact_integer",
"ilp_friendly",
"np_search"
] | Factoring N! into N large factors (Erdos-Guy-Selfridge).
Let N = 9545. Write N! as a product of exactly N positive integers,
N! = a_1 * a_2 * ... * a_N,
such that every factor satisfies a_i >= 3118. (The order of the factors does not matter; repeated values are
allowed.) The check is exact: the product of your n... | {"N": 9545, "t": 3118, "family": "ae_p38_factorial_factors", "subset": "construct"} | null | null | null | {"factors": [18708, 3118, 3118, 3118, 3118, 3118, 3119, 3119, 3119, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, ... | 1 |
construct-ae-p52-erdos-squarefree-l1-s0 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 1 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 71. Find a set A of distinct integers in {1, 2, ..., N} with 3 <= |A| <= 26 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer as JS... | {"N": 71, "t": 3, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57]} | 1 |
construct-ae-p52-erdos-squarefree-l1-s1 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 1 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 82. Find a set A of distinct integers in {1, 2, ..., N} with 4 <= |A| <= 28 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer as JS... | {"N": 82, "t": 4, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82]} | 1 |
construct-ae-p52-erdos-squarefree-l1-s2 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 1 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 91. Find a set A of distinct integers in {1, 2, ..., N} with 4 <= |A| <= 28 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer as JS... | {"N": 91, "t": 4, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82]} | 1 |
construct-ae-p52-erdos-squarefree-l1-s3 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 1 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 39. Find a set A of distinct integers in {1, 2, ..., N} with 2 <= |A| <= 24 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer as JS... | {"N": 39, "t": 2, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32]} | 1 |
construct-ae-p52-erdos-squarefree-l1-s4 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 1 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 54. Find a set A of distinct integers in {1, 2, ..., N} with 2 <= |A| <= 24 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer as JS... | {"N": 54, "t": 2, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32]} | 1 |
construct-ae-p52-erdos-squarefree-l1-s5 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 1 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 80. Find a set A of distinct integers in {1, 2, ..., N} with 3 <= |A| <= 26 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer as JS... | {"N": 80, "t": 3, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57]} | 1 |
construct-ae-p52-erdos-squarefree-l1-s6 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 1 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 66. Find a set A of distinct integers in {1, 2, ..., N} with 3 <= |A| <= 26 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer as JS... | {"N": 66, "t": 3, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57]} | 1 |
construct-ae-p52-erdos-squarefree-l1-s7 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 1 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 40. Find a set A of distinct integers in {1, 2, ..., N} with 2 <= |A| <= 24 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer as JS... | {"N": 40, "t": 2, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32]} | 1 |
construct-ae-p52-erdos-squarefree-l1-s8 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 1 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 84. Find a set A of distinct integers in {1, 2, ..., N} with 4 <= |A| <= 28 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer as JS... | {"N": 84, "t": 4, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82]} | 1 |
construct-ae-p52-erdos-squarefree-l1-s9 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 1 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 55. Find a set A of distinct integers in {1, 2, ..., N} with 2 <= |A| <= 24 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer as JS... | {"N": 55, "t": 2, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32]} | 1 |
construct-ae-p52-erdos-squarefree-l2-s0 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 2 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 101. Find a set A of distinct integers in {1, 2, ..., N} with 4 <= |A| <= 28 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer as J... | {"N": 101, "t": 4, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82]} | 1 |
construct-ae-p52-erdos-squarefree-l2-s1 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 2 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 124. Find a set A of distinct integers in {1, 2, ..., N} with 5 <= |A| <= 30 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer as J... | {"N": 124, "t": 5, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107]} | 1 |
construct-ae-p52-erdos-squarefree-l2-s2 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 2 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 361. Find a set A of distinct integers in {1, 2, ..., N} with 15 <= |A| <= 50 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer as ... | {"N": 361, "t": 15, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357]} | 1 |
construct-ae-p52-erdos-squarefree-l2-s3 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 2 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 156. Find a set A of distinct integers in {1, 2, ..., N} with 6 <= |A| <= 32 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer as J... | {"N": 156, "t": 6, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132]} | 1 |
construct-ae-p52-erdos-squarefree-l2-s4 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 2 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 241. Find a set A of distinct integers in {1, 2, ..., N} with 10 <= |A| <= 40 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer as ... | {"N": 241, "t": 10, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232]} | 1 |
construct-ae-p52-erdos-squarefree-l2-s5 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 2 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 293. Find a set A of distinct integers in {1, 2, ..., N} with 12 <= |A| <= 44 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer as ... | {"N": 293, "t": 12, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282]} | 1 |
construct-ae-p52-erdos-squarefree-l2-s6 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 2 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 151. Find a set A of distinct integers in {1, 2, ..., N} with 6 <= |A| <= 32 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer as J... | {"N": 151, "t": 6, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132]} | 1 |
construct-ae-p52-erdos-squarefree-l2-s7 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 2 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 102. Find a set A of distinct integers in {1, 2, ..., N} with 4 <= |A| <= 28 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer as J... | {"N": 102, "t": 4, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82]} | 1 |
construct-ae-p52-erdos-squarefree-l2-s8 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 2 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 207. Find a set A of distinct integers in {1, 2, ..., N} with 9 <= |A| <= 38 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer as J... | {"N": 207, "t": 9, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207]} | 1 |
construct-ae-p52-erdos-squarefree-l2-s9 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 2 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 127. Find a set A of distinct integers in {1, 2, ..., N} with 5 <= |A| <= 30 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer as J... | {"N": 127, "t": 5, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107]} | 1 |
construct-ae-p52-erdos-squarefree-l3-s0 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 3 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 718. Find a set A of distinct integers in {1, 2, ..., N} with 29 <= |A| <= 78 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer as ... | {"N": 718, "t": 29, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357, 382, 407, 432, 457, 482, 507, 532, 557, 582, 607, 632, 657, 682, 707]} | 1 |
construct-ae-p52-erdos-squarefree-l3-s1 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 3 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 427. Find a set A of distinct integers in {1, 2, ..., N} with 17 <= |A| <= 54 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer as ... | {"N": 427, "t": 17, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357, 382, 407]} | 1 |
construct-ae-p52-erdos-squarefree-l3-s2 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 3 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 1344. Find a set A of distinct integers in {1, 2, ..., N} with 54 <= |A| <= 128 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer a... | {"N": 1344, "t": 54, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357, 382, 407, 432, 457, 482, 507, 532, 557, 582, 607, 632, 657, 682, 707, 732, 757, 782, 807, 832, 857, 882, 907, 932, 957, 982, 1007, 1032, 1057, 1082, 1107, 1132, 1157, 1182, 1207, 1232, 1257, 1282, 1307, 1332]} | 1 |
construct-ae-p52-erdos-squarefree-l3-s3 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 3 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 686. Find a set A of distinct integers in {1, 2, ..., N} with 28 <= |A| <= 76 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer as ... | {"N": 686, "t": 28, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357, 382, 407, 432, 457, 482, 507, 532, 557, 582, 607, 632, 657, 682]} | 1 |
construct-ae-p52-erdos-squarefree-l3-s4 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 3 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 1214. Find a set A of distinct integers in {1, 2, ..., N} with 49 <= |A| <= 118 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer a... | {"N": 1214, "t": 49, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357, 382, 407, 432, 457, 482, 507, 532, 557, 582, 607, 632, 657, 682, 707, 732, 757, 782, 807, 832, 857, 882, 907, 932, 957, 982, 1007, 1032, 1057, 1082, 1107, 1132, 1157, 1182, 1207]} | 1 |
construct-ae-p52-erdos-squarefree-l3-s5 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 3 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 790. Find a set A of distinct integers in {1, 2, ..., N} with 32 <= |A| <= 84 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer as ... | {"N": 790, "t": 32, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357, 382, 407, 432, 457, 482, 507, 532, 557, 582, 607, 632, 657, 682, 707, 732, 757, 782]} | 1 |
construct-ae-p52-erdos-squarefree-l3-s6 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 3 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 1320. Find a set A of distinct integers in {1, 2, ..., N} with 53 <= |A| <= 126 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer a... | {"N": 1320, "t": 53, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357, 382, 407, 432, 457, 482, 507, 532, 557, 582, 607, 632, 657, 682, 707, 732, 757, 782, 807, 832, 857, 882, 907, 932, 957, 982, 1007, 1032, 1057, 1082, 1107, 1132, 1157, 1182, 1207, 1232, 1257, 1282, 1307]} | 1 |
construct-ae-p52-erdos-squarefree-l3-s7 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 3 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 1212. Find a set A of distinct integers in {1, 2, ..., N} with 49 <= |A| <= 118 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer a... | {"N": 1212, "t": 49, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357, 382, 407, 432, 457, 482, 507, 532, 557, 582, 607, 632, 657, 682, 707, 732, 757, 782, 807, 832, 857, 882, 907, 932, 957, 982, 1007, 1032, 1057, 1082, 1107, 1132, 1157, 1182, 1207]} | 1 |
construct-ae-p52-erdos-squarefree-l3-s8 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 3 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 1067. Find a set A of distinct integers in {1, 2, ..., N} with 43 <= |A| <= 106 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer a... | {"N": 1067, "t": 43, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357, 382, 407, 432, 457, 482, 507, 532, 557, 582, 607, 632, 657, 682, 707, 732, 757, 782, 807, 832, 857, 882, 907, 932, 957, 982, 1007, 1032, 1057]} | 1 |
construct-ae-p52-erdos-squarefree-l3-s9 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 3 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 694. Find a set A of distinct integers in {1, 2, ..., N} with 28 <= |A| <= 76 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer as ... | {"N": 694, "t": 28, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357, 382, 407, 432, 457, 482, 507, 532, 557, 582, 607, 632, 657, 682]} | 1 |
construct-ae-p52-erdos-squarefree-l4-s0 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 4 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 2767. Find a set A of distinct integers in {1, 2, ..., N} with 111 <= |A| <= 242 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer ... | {"N": 2767, "t": 111, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357, 382, 407, 432, 457, 482, 507, 532, 557, 582, 607, 632, 657, 682, 707, 732, 757, 782, 807, 832, 857, 882, 907, 932, 957, 982, 1007, 1032, 1057, 1082, 1107, 1132, 1157, 1182, 1207, 1232, 1257, 1282, 1307, 1332, 1357, 1382, 1407, 1432, 1457, 1482... | 1 |
construct-ae-p52-erdos-squarefree-l4-s1 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 4 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 3626. Find a set A of distinct integers in {1, 2, ..., N} with 145 <= |A| <= 310 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer ... | {"N": 3626, "t": 145, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357, 382, 407, 432, 457, 482, 507, 532, 557, 582, 607, 632, 657, 682, 707, 732, 757, 782, 807, 832, 857, 882, 907, 932, 957, 982, 1007, 1032, 1057, 1082, 1107, 1132, 1157, 1182, 1207, 1232, 1257, 1282, 1307, 1332, 1357, 1382, 1407, 1432, 1457, 1482... | 1 |
construct-ae-p52-erdos-squarefree-l4-s2 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 4 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 3700. Find a set A of distinct integers in {1, 2, ..., N} with 148 <= |A| <= 316 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer ... | {"N": 3700, "t": 148, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357, 382, 407, 432, 457, 482, 507, 532, 557, 582, 607, 632, 657, 682, 707, 732, 757, 782, 807, 832, 857, 882, 907, 932, 957, 982, 1007, 1032, 1057, 1082, 1107, 1132, 1157, 1182, 1207, 1232, 1257, 1282, 1307, 1332, 1357, 1382, 1407, 1432, 1457, 1482... | 1 |
construct-ae-p52-erdos-squarefree-l4-s3 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 4 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 2865. Find a set A of distinct integers in {1, 2, ..., N} with 115 <= |A| <= 250 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer ... | {"N": 2865, "t": 115, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357, 382, 407, 432, 457, 482, 507, 532, 557, 582, 607, 632, 657, 682, 707, 732, 757, 782, 807, 832, 857, 882, 907, 932, 957, 982, 1007, 1032, 1057, 1082, 1107, 1132, 1157, 1182, 1207, 1232, 1257, 1282, 1307, 1332, 1357, 1382, 1407, 1432, 1457, 1482... | 1 |
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