Mathematics
Open problems, research attempts and community review.
Provisional editorial order for Top Open Problems: Millennium Prize Problems first, followed by assessed difficulty tiers; the unassessed remainder keeps its previous catalogue order. About rankings
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- Math-4151 Vandiver's conjecture
- Math-4152 Congruent numbers in residue classes 5, 6, and 7 modulo 8
- Math-4153 L-value criterion for congruent numbers
- Math-4154 Infinitude of rational points on an elliptic curve
- Math-4155 Bounded prime-sum criterion for rational points
- Math-4156 Prime-sum growth and elliptic-curve rank
- Math-4157 Complex continuation of the associated zeta function
- Math-4158 Alternative and arithmetic proofs of the pi identities
- Math-4159 Odd-prime-power periodicity conjecture
- Math-4160 Power-of-two periodicity conjecture
- Math-4161 Arnold sequence as an f-transform
- Math-4162 Existence of a four-dimensional Euler brick
- Math-4163 Rational distances from the vertices of a square
- Math-4164 Factor RSA-1024
- Math-4165 Semi-magic square of distinct positive cubes
- Math-4166 Büchi's problem
- Math-4167 Carmichael's totient function conjecture
- Math-4168 Catalan–Dickson conjecture on aliquot sequences
- Math-4169 Are there any pairs of betrothed numbers which have same parity
- Math-4170 Are there any pairs of relatively prime amicable numbers
- Math-4171 Are there infinitely many betrothed numbers
- Math-4172 Do any odd noncototients exist
- Math-4173 Do any (2, 5)-perfect numbers exist
- Math-4174 Do any Taxicab(5, 2, n) exist for n > 1
- Math-4175 Pollock's tetrahedral-number conjecture
- Math-4176 Lang and Trotter's conjecture
- Math-4177 Characterize all algebraic number fields that have some power basis
- Math-4178 Find the value of the De Bruijn–Newman constant
- Math-4179 First Hardy–Littlewood zeta-function conjecture
- Math-4180 Piltz divisor problem
- Math-4181 Selberg's orthogonality conjecture
- Math-4182 The n-conjecture
- Math-4183 Does every rational number with an odd denominator have an odd greedy expansion
- Math-4184 Hartmanis–Stearns conjecture
- Math-4185 Wikipedia number-theory item 104: Congruent number problem (a corollary to Birch and Swinnerton-Dyer conjecture, per Tunnell's theorem…
- Math-4186 Erdős–Moser problem
- Math-4187 Goormaghtigh conjecture
- Math-4188 Wikipedia number-theory item 109: The uniqueness conjecture for Markov numbers that every Markov number is the largest number in exact…
- Math-4189 Which integers can be written as the sum of three perfect cubes
- Math-4190 Agrawal's conjecture
- Math-4191 Dubner's conjecture
- Math-4192 Erdős–Mollin–Walsh conjecture
- Math-4193 Feit–Thompson conjecture
- Math-4194 Fortune's conjecture
- Math-4195 Quadratic bound in Linnik's least-prime problem
- Math-4196 New Mersenne conjecture
- Math-4197 Selfridge's conjecture
- Math-4198 Does the converse of Wolstenholme's theorem hold for all natural numbers
- Math-4199 Are all Euclid numbers square-free
- Math-4200 Are there any composite c satisfying 2^{c − 1} ≡ 1 (mod c^{2})