FC100OpenSet1

A random subset of 100 open research problems, drawn uniformly at random from all problems with the category research open tag.

Quoted from FormalConjectures/Subsets/FC100OpenSet1.lean in Formal Conjectures (Google DeepMind) at commit 2055e5ad, Apache-2.0.

The 100 statements the list names, numbered as it lists them, each linked to its problem's article.

Entries 1 to 20

• 1. OeisA308734.conjecture (research open), in Four-square conjecture with powers of 2, 3, and 5
• 2. Buchi.buchi_problem (research open), in Büchi's problem
• 3. Erdos200.erdos_200 (research open), in Erdős Problem 200
• 4. Green31.green_31.variants.upper_eventually (research open), in Ben Green's Open Problem 31
• 5. Equidistribution.isAccumulationPoint_three_halves_pow (research open), in Equidistributed Sequences
• 6. Koethe.KotherConjecture.variants.matrixOver_KotherRadical (research open), in Köthe conjecture
• 7. Erdos535.erdos_535.variants.first_open_case (research open), in Erdős Problem 535
• 8. LychrelNumbers.no_lychrel_numbers_base10 (research open), in Lychrel numbers in base 10
• 9. Erdos830.erdos_830.parts.ii (research open), in Erdős Problem 830
• 10. Erdos125.erdos_125.variants.positive_unequal_density (research solved), in Erdős Problem 125
• 11. Erdos1113.erdos_1113.variants.filaseta_finch_kozek (research open), in Erdős Problem 1113
• 12. Erdos539.erdos_539.variants.isBigO_sq (research solved), in Erdős Problem 539
• 13. RiemannZetaValues.irrational_five (research solved), in Particular values of the Riemann zeta function
• 14. Erdos1074.erdos_1074.parts.ii (research open), in Erdős Problem 1074
• 15. Erdos282.erdos_282.variants.general (research open), in Erdős Problem 282
• 16. PellNumbers.infinite_pellNumber_primes (research open), in Infinitude of Pell number primes
• 17. ClassNumberProblem.class_number_problem (research open), in Class number problem for real quadratic fields
• 18. Grimm.grimm_conjecture_weak (research open), in Grimm's conjecture
• 19. OeisA63880.mod_216_of_a (research open), in Conjectures associated with A063880
• 20. Green24.green_24 (research open), in Green's Open Problem 24

Entries 21 to 40

• 21. Erdos12.erdos_12.parts.iii (research open), in Erdős Problem 12
• 22. Erdos288.erdos_288.variants.exists_k_gt_2 (research open), in Erdős Problem 288
• 23. EllipticCurveRank.RatEllipticCurve.twentyone_le_rank_height_count_asymptotic (research open), in Some conjectures about ranks of elliptic curves over ℚ
• 24. Erdos647.erdos_647.variants.lim (research open), in Erdős Problem 647
• 25. Selfridge.selfridge_conjecture (research open), in Selfridge's conjectures
• 26. Erdos887.erdos_887.parts.i (research open), in Erdős Problem 887
• 27. Erdos340.erdos_340.variants.co_density_zero_sub (research open), in Erdős Problem 340
• 28. Erdos694.erdos_694.variants.carmichael (research open), in Erdős Problem 694
• 29. Mathoverflow1973.mathoverflow_1973 (research solved), in Mathoverflow 1973
• 30. Erdos479.erdos_479 (research open), in Erdős Problem 479
• 31. OeisA67720.prime_add_one_of_a (research open), in Conjectures associated with A067720
• 32. Erdos1092.f_asymptotic_general (research solved), in Erdős Problem 1092
• 33. Erdos1074.erdos_1074.parts.iv (research open), in Erdős Problem 1074
• 34. Green9.green_9_iii (research open), in Green's Open Problem 9
• 35. Erdos770.erdos_770.variants.three (research open), in Erdős Problem 770
• 36. Erdos137.erdos_137.variants.multiple_powerful_factors (research open), in Erdős Problem 137
• 37. Irrational.irrational_e_to_e (research open), in Open questions on irrationality of numbers
• 38. Erdos324.erdos_324 (research open), in Erdős Problem 324
• 39. Erdos329.erdos_329 (research open), in Erdős Problem 329: Maximum Density of Sidon Sets
• 40. Transcendental.pi_pow_pi_pow_pi_transcendental (research open), in Open questions on transcendence of numbers

Entries 41 to 60

• 41. Erdos409.erdos_409.parts.i.isBigO (research open), in Erdős Problem 409
• 42. Arxiv.«2501.03234».conjecture_4_1 (research open), in An Arithmetic Sum Associated with the Classical Theta Function
• 43. MonochromaticQuantumGraph.eqSystem10_no_solution_d3 (research open), in Monochromatic quantum graphs (inherited vertex colorings)
• 44. PoincareConjecture.poincare_conjecture.variants.smooth_dimension_four (research open), in The Poincaré Conjecture
• 45. Transcendental.pi_pow_sqrt_two_transcendental (research open), in Open questions on transcendence of numbers
• 46. OeisA303656.conjecture (research open), in Sum of two squares, a power of 3, and a power of 5
• 47. Erdos517.erdos_517 (research open), in Erdős Problem 517
• 48. MonochromaticQuantumGraph.eqSystem16_no_solution_d3 (research open), in Monochromatic quantum graphs (inherited vertex colorings)
• 49. Arxiv.«0912.2382».curling_number_conjecture (research open), in The Curling Number Conjecture
• 50. Grimm.grimm_conjecture (research open), in Grimm's conjecture
• 51. Erdos272.erdos_272.variants.szabo_strong (research open), in Erdős Problem 272
• 52. UnionClosed.union_closed.variants.cardinality_even_of_union_closed_tight (research open), in Union-closed sets conjecture
• 53. MonochromaticQuantumGraph.eqSystem12_no_solution_d3 (research open), in Monochromatic quantum graphs (inherited vertex colorings)
• 54. Erdos1097.erdos_1097 (research solved), in Erdős Problem 1097
• 55. MonochromaticQuantumGraph.eqSystem_no_solution_ge6_ge3_real (research open), in Monochromatic quantum graphs (inherited vertex colorings)
• 56. Erdos952.erdos_952 (research solved), in Erdős Problem 952
• 57. Green58.green_58 (research open), in Ben Green's Open Problem 58
• 58. Erdos329.erdos_329.variants.converse_implication (research open), in Erdős Problem 329: Maximum Density of Sidon Sets
• 59. Mandelbrot.MLC (research open), in Conjectures about the Mandelbrot and Multibrot sets
• 60. Erdos890.erdos_890.parts.a (research open), in Erdős Problem 890

Entries 61 to 80

• 61. Erdos1002.erdos_1002 (research open), in Erdős Problem 1002
• 62. Erdos188.erdos_188 (research open), in Erdős Problem 188
• 63. BabaiSeressConjectures.babai_seress_conjecture_alternating (research open), in Babai–Seress Conjectures on the Diameter of Finite Groups
• 64. OpenQuantumProblem23.hasSICPOVM_60 (research open), in Open Quantum Problem 23: SIC-POVMs
• 65. Erdos23.erdos_23 (research open), in Erdős Problem 23
• 66. Gilbreath.gilbreath_conjecture (research open), in Gilbreath's conjecture
• 67. Erdos313.erdos_313 (research open), in Erdős Problem 313
• 68. Green14.W_3_39_lower (research solved), in Ben Green's Open Problem 14
• 69. Erdos931.erdos_931.variants.exists_prime (research open), in Erdős Problem 931
• 70. Erdos398.erdos_398 (research open), in Erdős Problem 398
• 71. Erdos61.erdos_61 (research open), in Erdős Problem 61 -- Erdős–Hajnal Conjecture
• 72. Erdos996.erdos_996 (research open), in Erdős Problem 996
• 73. Erdos695.erdos_695 (research open), in Erdős Problem 695
• 74. MonochromaticQuantumGraph.eqSystem10_no_solution_d3_trinary_int (research solved), in Monochromatic quantum graphs (inherited vertex colorings)
• 75. Erdos92.erdos_92.variants.weak (research solved), in Erdős Problem 92
• 76. RamseyNumbers.ramsey_number_five_five (research open), in Ramsey numbers
• 77. Erdos385.erdos_385.parts.ii (research open), in Erdős Problem 385
• 78. LittlewoodConjecture.padic_littlewood_conjecture (research open), in Littlewood conjectures
• 79. Mandelbrot.volume_frontier_mandelbrotSet_eq_zero (research open), in Conjectures about the Mandelbrot and Multibrot sets
• 80. Erdos358.erdos_358.variants.prime_set (research open), in Erdős Problem 358

Entries 81 to 100

• 81. OeisA80170.gcdCondition_iff_primePowerCondition (research solved), in Conjecture relating two characterizations of a set of integers.
• 82. Erdos332.erdos_332 (research open), in Erdős Problem 332
• 83. Green14.W_3_37_lower (research solved), in Ben Green's Open Problem 14
• 84. EulerBrick.cuboidThree (research open), in Open questions regarding the existence of Euler bricks
• 85. Erdos269.erdos_269.variants.rational (research open), in Erdős Problem 269
• 86. Arxiv.«1601.03081».crystals_components_unique (research open), in Unique Crystal Components
• 87. Erdos123.erdos_123.variants.powers_2_3_5_snug (research open), in Erdős Problem 123
• 88. SumOfThreeCubes.isSumOfThreeCubes_iff_mod_9 (research open), in Sum of three cubes
• 89. WrittenOnTheWallII.GraphConjecture327.conjecture327 (research solved), in Written on the Wall II - Conjecture 327
• 90. WrittenOnTheWallII.GraphConjecture316.conjecture316 (research solved), in Written on the Wall II - Conjecture 316
• 91. Erdos888.erdos_888 (research solved), in Erdős Problem 888
• 92. Erdos260.erdos_260 (research solved), in Erdős Problem 260
• 93. Erdos36.erdos_36.variants.lower (research open), in Erdős Problem 36
• 94. MonochromaticQuantumGraph.eqSystem10_no_solution_d4 (research open), in Monochromatic quantum graphs (inherited vertex colorings)
• 95. Superperfect.twoFivePerfect (research open), in (m,k)-perfect numbers
• 96. Erdos307.erdos_307 (research open), in Erdős Problem 307
• 97. MonochromaticQuantumGraph.eqSystem6_no_solution_d4 (research solved), in Monochromatic quantum graphs (inherited vertex colorings)
• 98. OeisA41.noPowerPartitionNumber (research open), in No powers as partition numbers
• 99. Erdos1093.erdos_1093.parts.ii (research open), in Erdős Problem 1093
• 100. Green61.green_61 (research open), in Ben Green's Open Problem 61

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