Unsolved problems in number theory

positive integer which equals the sum of all its divisors

Conjecture that every even integer greater than 2 is the sum of two primes

conjecture in mathematics linked to the repartition of prime numbers

prime number of the form 2ⁿ−1

mathematical constant; limiting difference between the harmonic series and the natural logarithm; equal to ca 0.577

prime either 2 more or 2 less than another prime

positive integer of the form (2^(2^n))+1

conjecture in mathematics that concerns sequences

number theory conjecture

problem in number theory

number in the Lucas sequence where each number is the sum of the two preceding it (2, 1, 3, 4, 7, 11, ...)

four basic unsolved problems about prime numbers: Goldbach’s conjecture; twin prime conjecture; Legendre’s conjecture; whether there are infinitely many primes of the form 𝑛²+1

number of the form n*(2^n)+1

conjecture

prime number that is also a palindromic number

hypothetical number whose sum of divisors is twice the number plus 1

denominator of close rational approximation to the square root of 2

Type of prime number

conjecture that there is a prime between any two square numbers

the Diophantine problem of finding an integer, whose factorial plus one is a perfect square

pair of prime numbers that differ by 6

number k which k*2^n+1 is composite with all n

Type of prime number

number

natural number of the form n2^n − 1

conjecture

unproven statement in number theory

conjecture in number theory

numbers of the form 2^{2^p-1}-1, where p and 2^p-1 are prime numbers

conjecture

type of prime number

conjecture

positive integer that is the area of a right triangle with three rational number sides

prime number of the form (2ⁿ+1)/3, where n is another prime

problem of counting integer points within a circle of given radius centered at the origin

pair of prime numbers that differ by 4

prime such that p² divides 2ᵖ⁻¹-1

cuboid whose edges and face diagonals have integer lengths

conjecture on the pattern of forward differences of the sequence of prime numbers

number that is one more than the product of the first n prime numbers

positive integer which equals half of the sum of the divisors of the sum of its divisors

conjecture

natural number sharing its abundancy index with at least one other number

odd natural number k such that k·2^n − 1 is composite for all natural n

number theory conjecture

in numbers theory, a given integer a which is not a perfect square and not −1 is a primitive root modulo infinitely many primes p

conjecture that gives a criterion for a univariate integer-coefficient polynomial to give infinitely many prime values

prime number in the Fibonacci sequence

the mathematical problem of characterizing which integers are representable as sums of three cubes of integers

mathematical conjectures about Mersenne primes

set of three prime numbers in which the smallest and largest of the three differ by 6

bound on the gaps between prime numbers

conjecture about prime numbers

conjecture that any odd integer >5 equals an odd prime plus an even semiprime

on the distribution of prime numbers in arithmetic progressions

type of prime number conjectured to exist

prime number of the form 2ᵐ3ⁿ+1

four prime numbers of the form {p, p+2, p+6, p+8}