Wieferich prime

In mathematics, a Wilson prime is a certain kind of prime number. A prime p is called a Wilson prime if p² divides (p − 1)! + 1, where ! denotes the factorial function; compare this with Wilson's theorem, which states that every prime p divides (p − 1)! + 1. The only known Wilson primes are 5, 13, and 563 (sequence A007540 in OEIS); if any others exist, they must be greater than 5 · 108. It has been conjectured that infinitely many Wilson primes exist, and that the number of Wilson primes in an interval [x, ...

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List of number theory topics - Primality tests. Prime factorization algorithm Trial division Sieve of Eratosthenes Probabilistic algorithm Fermat primality test Pseudoprime Carmichael number Euler pseudoprime Euler-Jacobi pseudoprime Fibonacci pseudoprime Probable prime Miller-Rabin primality test Lucas-Lehmer primality test Lucas-Lehmer test for Mersenne numbers AKS prim ...

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List of number theory topics, List of number theory topics - Factors, List of number theory topics - Fractions, List of number theory topics - Modular arithmetic, List of number theory topics - Arithmetic functions, List of number theory topics - Analytic number theory: additive problems, List of number theory topics - Algebraic number theory, List of number theory topics - Quadratic forms, List of number theory topics - L-functions, List of number theory topics - Diophantine equations, List of number theory topics - Diophantine approximation, List of number theory topics - Sieve methods, List of number theory topics - Named primes, List of number theory topics - Combinatorial number theory, List of number theory topics - Computational number theory, List of number theory topics - Primality tests, List of number theory topics - Integer factorization, List of number theory topics - Pseudo-random numbers, List of number theory topics - History

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