Category
Problem Set
Status
Agoh-Giuga Conjecture
Is $p$ prime if and only if $pB_{p-1} \equiv -1 \pmod{p}$ for the Bernoulli number $B_{p-1}$?...
Elliott-Halberstam Conjecture
Do primes distribute uniformly in arithmetic progressions up to nearly $x$ (instead of $x^{1/2}$)?...
Singmaster's Conjecture
Is there a finite upper bound on multiplicities of entries >1 in Pascal's triangle?...
Odd Perfect Numbers
Do any odd perfect numbers exist?...
Infinitude of Perfect Numbers
Are there infinitely many perfect numbers?...
Quasiperfect Numbers
Do quasiperfect numbers exist?...
Lychrel Numbers
Do Lychrel numbers exist in base 10?...
Odd Weird Numbers
Do odd weird numbers exist?...
Infinitude of Amicable Pairs
Are there infinitely many pairs of amicable numbers?...
Pi Normality
Is π a normal number (all digits equally frequent in all bases)?...
Algebraic Number Normality
Are all irrational algebraic numbers normal?...
Gilbreath's Conjecture
Does iterating unsigned differences on prime sequence always yield 1 as first element?...
Lander-Parkin-Selfridge Conjecture
If Σᵢ aᵢᵏ = Σⱼ bⱼᵏ with m terms on left, n on right, is m+n ≥ k?...
Class Number Problem
Are there infinitely many real quadratic fields with class number 1 (unique factorization)?...
Hilbert's 12th Problem
Extend Kronecker-Weber theorem to abelian extensions of arbitrary number fields....
Leopoldt's Conjecture
Does the p-adic regulator of an algebraic number field never vanish?...
Siegel Zeros
Do Siegel zeros (real zeros of Dirichlet L-functions near s=1) exist?...
Schanuel's Conjecture
For e and π: are they algebraically independent? Is e+π, eπ, π^e, etc. transcendental?...
Euler-Mascheroni Constant Irrationality
Is the Euler-Mascheroni constant γ irrational? Transcendental?...
Littlewood Conjecture
For any α,β ∈ ℝ, is lim inf_{n→∞} n·||nα||·||nβ|| = 0?...
Four Exponentials Conjecture
If x₁,x₂ and y₁,y₂ are linearly independent over ℚ, is at least one of e^(xᵢyⱼ) transcendental?...
Integer Factorization Polynomial Time
Can integer factorization be done in polynomial time?...