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Unsolved problems in number theory

Table of contents

Agoh–Giuga conjecture

Andrica's conjecture

Artin's conjecture on primitive roots

Balanced prime

Bateman–Horn conjecture

Bunyakovsky conjecture

Carmichael's totient function conjecture

Casas-Alvero conjecture

Class number problem

Congruent number

Covering system

Cramér's conjecture

Dickson's conjecture

Elliott–Halberstam conjecture

Erdős–Turán conjecture on additive bases

Euler's constant

Feit–Thompson conjecture

Fibonacci prime

Firoozbakht's conjecture

Four exponentials conjecture

Gilbreath's conjecture

Gillies' conjecture

Goldbach's conjecture

Greenberg's conjectures

Grimm's conjecture

Grothendieck–Katz p-curvature conjecture

Hall's conjecture

Hermite's problem

Hilbert's ninth problem

Kummer–Vandiver conjecture

Landau's problems

Lehmer's totient problem

Lemoine's conjecture

Leopoldt's conjecture

Manin conjecture

Mersenne conjectures

Minimum overlap problem

Newman's conjecture

Odd greedy expansion

Oppermann's conjecture

Pierpont prime

Polignac's conjecture

Prime triplet

Problems involving arithmetic progressions

Regular prime

Safe and Sophie Germain primes

Schanuel's conjecture

Schinzel's hypothesis H

Sexy prime

Supersingular prime (algebraic number theory)

Twin prime

Vojta's conjecture

Wagstaff prime

Wall–Sun–Sun prime

Waring–Goldbach problem

Wieferich prime

Wolstenholme prime

 Ancestors (4)

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