FC100OpenSet2
A curated subset of 100 mathematically important open research conjectures with verified formal statements (
category research open), excluding sub-variants, OEIS sequences, and machine-generated graph conjectures.
Quoted from FormalConjectures/Subsets/FC100OpenSet2.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.
RiemannHypothesis.riemannHypothesis(research open), in Riemann Hypothesis and its generalizations - 2.
ComplexityTheory.P_ne_NP(research open), in Conjectures in Complexity Theory - 3.
GRH.generalized_riemann_hypothesis(research open), in Riemann Hypothesis and its generalizations - 4.
WeierstrassCurve.Affine.Rat.weakBSD(research open), in The Birch and Swinnerton-Dyer (BSD) Conjecture - 5.
NavierStokes.navier_stokes_existence_and_smoothness_R3(research open), in Existence And Smoothness Of The Navier–Stokes Equation - 6.
ABC.abc(research open), in *abc* conjecture - 7.
AlgebraicGeometry.resolution_of_singularities(research open), in Resolution of singularities - 8.
GoldbachConjecture.goldbach(research open), in Goldbach's conjecture - 9.
InverseGalois.inverse_galois_problem(research open), in Inverse Galois problem - 10.
PoincareConjecture.poincare_conjecture.variants.smooth_dimension_four(research open), in The Poincaré Conjecture - 11.
TwinPrimes.twin_primes(research open), in Twin prime conjecture - 12.
Kakeya.kakeya_set_conjecture(research open), in Kakeya problem - 13.
ComplexityTheory.NP_ne_coNP(research open), in Conjectures in Complexity Theory - 14.
Schinzel.schinzel_conjecture(research open), in Hypothesis H - 15.
HardyLittlewood.first_hardy_littlewood_conjecture(research open), in First Hardy–Littlewood conjecture - 16.
Mandelbrot.MLC(research open), in Conjectures about the Mandelbrot and Multibrot sets - 17.
LittlewoodConjecture.littlewood_conjecture(research open), in Littlewood conjectures - 18.
HasseWeil.exists_hasAnalyticContinuation(research open), in The Hasse--Weil conjecture for elliptic curves - 19.
Schanuel.schanuel_conjecture(research open), in Schanuel's Conjecture - 20.
Dickson.dickson_conjecture(research open), in Dickson's conjecture
Entries 21 to 40
- 21.
InvariantSubspaceProblem.Invariant_subspace_problem(research open), in Invariant Subspace Problem - 22.
EllipticCurveRank.RatEllipticCurve.unbounded_rank_conjecture(research open), in Some conjectures about ranks of elliptic curves over ℚ - 23.
BatemanHornConjecture.bateman_horn_conjecture(research open), in Bateman-Horn Conjecture - 24.
LocalUniformization.local_uniformization(research open), in Local uniformization - 25.
ElliottHalberstamConjecture.elliott_halberstam(research open), in Elliott–Halberstam conjecture - 26.
Arxiv.«math.0703548».projective_module_isStablyFree(research open), in Algebraic consequences of the Farrell–Jones conjecture - 27.
Erdos61.erdos_61(research open), in Erdős Problem 61 -- Erdős–Hajnal Conjecture - 28.
SerreUniformity.serre_uniformity(research open), in Serre's uniformity conjecture over the rationals - 29.
ClassNumberProblem.class_number_problem(research open), in Class number problem for real quadratic fields - 30.
Arxiv.id2303_01089.conjecture_1_3(research open), in Furstenberg's `times p, times q` conjectures - 31.
Irrational.algebraicIndependent_e_pi(research open), in Open questions on irrationality of numbers - 32.
Bunyakovsky.bunyakovsky_conjecture(research open), in Bunyakovsky conjecture - 33.
Erdos52.erdos_52(research open), in Erdős Problem 52 - 34.
PolyTime.isPolyTime_primeFactorsList(research open), in Polynomial-time computability of factoring - 35.
ZagierMZV.zagier_conjecture(research open), in Zagier's Conjecture on Multiple Zeta Values - 36.
LegendreConjecture.legendre_conjecture(research open), in Legendre's conjecture - 37.
KummerVandiver.kummer_vandiver(research open), in Kummer–Vandiver conjecture - 38.
RegularPrimes.regularprime_conjecture(research open), in Infinite Regular Primes - 39.
JacobianConjecture.jacobian_conjecture_two_variables(research open), in Jacobian conjecture - 40.
ArtinPrimitiveRootsConjecture.artin_primitive_roots.parts.i(research open), in Artin's conjecture on primitive roots
Entries 41 to 60
- 41.
Catalan.pillais_conjecture(research open), in Catalan's conjecture and related Diophantine equations - 42.
Hadamard.HadamardConjecture(research open), in Hadamard's conjecture - 43.
VaughtConjecture.vaught_conjecture(research open), in Vaught conjecture - 44.
AlgebraicNormality.irrational_algebraic_absolutely_normal(research open), in Normality of Irrational Algebraic Numbers - 45.
LehmerMahlerMeasureProblem.lehmer_mahler_measure_problem(research open), in Lehmer's Mahler measure problem - 46.
RiemannZetaValues.irrational_odd(research open), in Particular values of the Riemann zeta function - 47.
BeckFiala.beck_fiala_conjecture(research open), in Beck–Fiala theorem and conjecture - 48.
RamanujanTau.lehmer_ramanujan_tau(research open), in Ramanujan τ-function - 49.
UnionClosed.union_closed(research open), in Union-closed sets conjecture - 50.
Erdos28.erdos_28(research open), in Erdős Problem 28 - 51.
GaussCircleProblem.error_isBigO(research open), in Gauss circle problem - 52.
PrimesAndPerfectSquares.infinite_prime_sq_add_one(research open), in Primes and perfect squares - 53.
BabaiSeressConjectures.babai_seress_conjecture(research open), in Babai–Seress Conjectures on the Diameter of Finite Groups - 54.
TarskiExponentialFunctionProblem.tarski_exponential_function_problem(research open), in Tarski's exponential function problem - 55.
Margulis.conjecture_1_1(research open), in A conjecture by Margulis on matrix groups - 56.
Exponentials.four_exponentials_conjecture(research open), in Exponentials conjectures and theorems - 57.
HopfAlgebraCohomology.cohomologyRing_finiteType(research open), in Finite generation of the cohomology of finite-dimensional Hopf algebras - 58.
Erdos723.erdos_723(research open), in Erdős Problem 723: The prime power conjecture. - 59.
AndrewsCurtis.andrews_curtis_conjecture(research open), in The Andrews-Curtis conjecture - 60.
GapConjecture.gap_conjecture(research open), in Gap conjecture
Entries 61 to 80
- 61.
InscribedSquare.inscribed_square_problem(research open), in Inscribed square problem - 62.
Bugeaud08.problem_10_8(research open), in Bugeaud Collection of Conjectures and Open Questions: \(p\)-adic Littlewood Conjecture - 63.
Erdos107.erdos_107(research open), in Erdős Problem 107 - 64.
BealConjecture.beal_conjecture(research open), in Beal conjecture - 65.
FermatCatalanConjecture.fermat_catalan(research open), in Fermat-Catalan conjecture - 66.
PerfectNumbers.odd_perfect_number_conjecture(research open), in Perfect numbers - 67.
Jacobson.jacobson_conjecture(research open), in Jacobson Conjecture - 68.
LonelyRunnerConjecture.lonely_runner_conjecture(research open), in Lonely runner conjecture - 69.
Erdos234.erdos_234(research open), in Erdős Problem 234 - 70.
Fermat.infinite_fermat_primes(research open), in Open questions about Fermat numbers - 71.
PierceBirkhoff.pierce_birkhoff_conjecture(research open), in Pierce–Birkhoff conjecture - 72.
Erdos1029.erdos_1029(research open), in Erdős Problem 1029 - 73.
Hall.weak_hall_conjecture(research open), in Hall's conjecture - 74.
RudinsConjecture.rudins_conjecture(research open), in Rudin's conjecture on squares in arithmetic progressions - 75.
Mersenne.infinitely_many_mersenne_primes(research open), in Conjectures about Mersenne primes - 76.
Erdos572.erdos_572(research open), in Erdős Problem 572 - 77.
Transcendental.exp_add_pi_transcendental(research open), in Open questions on transcendence of numbers - 78.
Erdos510.erdos_510(research open), in Erdős Problem 510 - 79.
Green50.green_50(research open), in Ben Green's Open Problem 50 - 80.
Erdos242.erdos_242(research open), in Erdős Problem 242
Entries 81 to 100
- 81.
Equidistribution.isEquidistributedModuloOne_three_halves_pow(research open), in Equidistributed Sequences - 82.
ReedOmegaDeltaChi.reed_omega_delta_chi_conjecture_for_finite_graphs(research open), in Reed's omega, delta, and chi conjecture - 83.
BingBorsuk.bing_borsuk_conjecture(research open), in The Bing-Borsuk Conjecture - 84.
CollatzConjecture.collatz_conjecture(research open), in Collatz conjecture - 85.
OpenQuantumProblem23.sicPOVMs(research open), in Open Quantum Problem 23: SIC-POVMs - 86.
Arxiv.«math.0110202».banach_mazur_rotation_problem(research open), in Banach-Mazur Rotation Problem - 87.
Erdos5.erdos_5(research open), in Erdős Problem 5 - 88.
Conjecture_1_3_to_2_3.conjecture_1_3_to_2_3(research open), in The \(\frac 1 3\)–\(\frac 2 3\) conjecture - 89.
FibonacciPrimes.fib_primes_infinite(research open), in Fibonacci Primes - 90.
Singmaster.singmaster(research open), in Singmaster's conjecture - 91.
Erdos562.erdos_562(research open), in Erdős Problem 562 - 92.
Erdos564.erdos_564(research open), in Erdős Problem 564 - 93.
Arxiv.«0805.3777».isGenericRank_of_le_critical(research open), in Generic and maximal rank of 3-tensors - 94.
PrimeTriplets.prime_triplets(research open), in Prime Triplet Conjecture - 95.
Erdos212.erdos_212(research open), in Erdős Problem 212 - 96.
Idoneal.idoneal_numbers_completeness(research open), in Idoneal numbers completeness conjecture - 97.
Erdos583.erdos_583(research open), in Erdős Problem 583 - 98.
Erdos233.erdos_233(research open), in Erdős Problem 233 - 99.
Bloch.blochConstant_exact_value(research open), in Bloch and Landau constants - 100.
Erdos714.erdos_714(research open), in Erdős Problem 714
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