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Unsolved problems in number theory

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idoneal number
Mathematical concept in prime numbers
Polignac's conjecture
conjecture in number theory involving prime gaps
Wolstenholme prime
prime number satisfying a certain congruence
Singmaster's conjecture
conjecture in combinatorial number theory
Giuga number
composite number n such that p divides n/p − 1 for every prime divisor p of n
lonely runner conjecture
number-theoretic conjecture that states that 𝑘 people running around a circular track with distinct speeds will each be, at some point, separated by ¹⁄ₖ from every other runner
Lindelöf hypothesis
conjecture
Schinzel's hypothesis H
number theory conjecture that, for any finite set of nonconstant irreducible integer polynomials with positive leading coefficients, either they are simultaneously prime infinitely often, or else a fixed divisor always divides at least one of them
Grimm's conjecture
Prime number conjecture
Goormaghtigh conjecture
conjecture
Hilbert's ninth problem
mathematical problem
Schanuel's conjecture
conjecture concerning the transcendence degree of field extensions of the rational numbers
Dickson's conjecture
Conjecture about prime numbers
Feit–Thompson conjecture
conjecture in number theory that there are no primes 𝑝≠𝑞 such that (𝑝^𝑞−1)/(𝑝−1) divides (𝑞^𝑝−1)/(𝑞−1)
Montgomery's pair correlation conjecture
mathematical conjecture stated by Hugh Montgomery
Hall's conjecture
conjecture
Carmichael's totient function conjecture
mathematics concept
Euclid–Mullin sequence
infinite sequence of prime numbers
Littlewood conjecture
Mathematical problem
Lehmer's totient problem
unsolved problem in mathematics
Tate conjecture
conjecture in algebraic geometry
divisor summatory function
Summatory function of the divisor-counting function
Baillie–PSW primality test
probabilistic primality testing algorithm
Gaussian moat
mathematical problem in number Theory
Bateman–Horn conjecture
conjecture in number theory
Szpiro's conjecture
conjecture in number theory
juggler sequence
sequence hypothesized to always terminate at 1
Covering system
collection of finitely many residue classes whose union contains every integer