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-450 Hilbert's Tenth Problem over C(t) with named t
- Math-469 Hall's Conjecture
- Math-475 Pi Normality
- Math-480 Are there only finite Fermat Primes?
- Math-487 Potential Density of Rational Points on K3 Surfaces
- Math-490 Koblitz Conjecture for Prime Orders of Elliptic Curves
- Math-505 A certified bound of 236 for bounded prime gaps
- Math-507 Irrationality of e+pi
- Math-509 Gilbreath's Conjecture
- Math-511 The Lonely Runner Conjecture
- Math-514 Brocard's Problem
- Math-515 The Erdős-Straus Conjecture
- Math-528 Sumsets Containing Composites
- Math-529 Sumsets of Perfect Squares
- Math-530 Products of Primes Modulo p
- Math-531 Multiplicatively Closed Set Density
- Math-532 Primes with p-2 Having Odd Omega
- Math-533 Difference Sets Containing Squares
- Math-534 Gaps Between Sums of Two Squares
- Math-538 Equidistribution of Integer Multiples
- Math-541 Bounds for Birch's Theorem
- Math-553 Covering by Residue Classes
- Math-554 Residue Class Multiple Coverage
- Math-555 Maximal Covering Interval
- Math-558 Catalan-Mersenne Conjecture
- Math-559 Singmaster's Conjecture
- Math-561 Firoozbakht's Conjecture
- Math-571 Grimm's Conjecture
- Math-572 Magic Square of Squares
- Math-573 Scholz Conjecture
- Math-574 Quasiperfect Numbers
- Math-575 Almost Perfect Numbers Beyond Powers of 2
- Math-576 The Number of Idoneal Numbers
- Math-577 Amicable Numbers of Opposite Parity
- Math-578 Infinitely Many Amicable Pairs
- Math-579 Infinitely Many Giuga Numbers
- Math-580 Lychrel Numbers in Base 10
- Math-581 Odd Weird Numbers
- Math-582 Is 10 a Solitary Number?
- Math-583 Lemoine's Conjecture
- Math-584 Recamán's Sequence Completeness
- Math-585 Class Number Problem
- Math-587 Agoh-Giuga Conjecture
- Math-634 Hardy-Littlewood Conjecture B (Second Conjecture)
- Math-635 The Prime Number Race
- Math-636 Shanks Chains of Length 7
- Math-637 Erdős Conjecture on Carmichael Numbers
- Math-638 Pomerance's Questions on Good Primes
- Math-639 Walking to Infinity on Gaussian Primes
- Math-640 Erdős Problem #1