Number theory
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-156 Normality of Irrational Algebraic Numbers
- Math-157 The Generalized Sato-Tate Conjecture for Higher-Dimensional Abelian Varieties
- Math-159 Global Gan–Gross–Prasad Conjecture (Fixed-Representation Form)
- Math-163 Uniform Subconvexity for Standard Automorphic L-Functions on GL(n)
- Math-165 Brauer–Manin Obstruction for Rationally Connected Varieties
- Math-170 Manins Conjecture on the Asymptotic Density of Rational Points on Fano Varieties
- Math-171 Cramer Conjecture on the Limsup of Normalized Prime Gaps
- Math-174 Tate's rational leading-term Stark conjecture
- Math-175 Algebraic independence of pi and e
- Math-177 Dirichlet's Divisor Problem
- Math-178 Simplicity of the Nontrivial Zeros of the Riemann Zeta Function
- Math-189 Transcendence of Apéry's Constant
- Math-194 Landau's Fourth Problem: Primes of the Form n² + 1
- Math-200 Parity conjecture for elliptic curves
- Math-201 Artin's Conjecture on Primitive Roots
- Math-202 The Abelian Rank-One Stark Conjecture
- Math-204 Exact Asymptotic Waring Function G(k)
- Math-210 Lehmer’s Mahler Measure Problem
- Math-212 Effective Roth Theorem
- Math-214 Brauer-Manin obstruction for number-field curves: Hasse-principle form
- Math-221 Skolem Problem
- Math-232 Breuil-Mezard conjecture: equality of the Galois and automorphic sides
- Math-234 Shafarevich Freeness Conjecture over Qab
- Math-240 Serre's Uniformity Problem for Elliptic Curves
- Math-243 Zagier's dimension conjecture for classical multiple zeta values
- Math-249 Odd Perfect Numbers
- Math-255 Dynamical Mordell–Lang Conjecture
- Math-264 The Gauss Circle Problem
- Math-265 Are there infinitely many Mersenne primes?
- Math-275 Zagier Conjecture on Dedekind Zeta Values
- Math-288 Frey-Mazur Conjecture
- Math-290 Irrationality of Euler's Constant
- Math-299 Montgomery's Large Value Conjecture for Dirichlet Polynomials
- Math-319 Fermat-Catalan Conjecture
- Math-325 Legendre's Conjecture
- Math-328 Iwasawa mu-invariant conjecture for number fields
- Math-330 Chowla Non-Vanishing Conjecture for Dirichlet L-Functions at the Central Point
- Math-331 Irrationality of zeta(5)
- Math-357 Kummer–Vandiver conjecture
- Math-360 Least quadratic nonresidue modulo a prime
- Math-370 Beal's Conjecture
- Math-377 Four Exponentials Conjecture
- Math-385 Partition Regularity of Pythagorean Triples
- Math-387 Brauer-Manin obstruction to the Hasse principle for K3 surfaces
- Math-394 Are There Infinitely Many Sophie Germain Primes?
- Math-417 Irrationality of Catalan’s Constant
- Math-431 Colmezs Conjecture on Faltings Heights of CM Abelian Varieties
- Math-432 Greenberg's Iwasawa-invariants conjecture
- Math-434 Sums of Three Cubes Representation Conjecture
- Math-442 Piltz Divisor Problem for k-Fold Divisor Error Terms