Clement’s theorem on twin primes

Theorem. (P. Clement) Given a prime numberMathworldPlanetmath p, p+2 is also a prime (and p and p+2 form a twin primeMathworldPlanetmath) if and only if 4(p-1)!-4-p(modp2+2p).

Richard Crandall and Carl Pomerance see this theorem as “a way to connect the notion of twin-prime pairs with the Wilson-Lagrange theorem.”


  • 1 Richard Crandall & Carl Pomerance, Prime Numbers: A Computational Perspective, 2nd Edition. New York: Springer (2005): 65, Exercise 1.57
Title Clement’s theorem on twin primes
Canonical name ClementsTheoremOnTwinPrimes
Date of creation 2013-03-22 17:58:32
Last modified on 2013-03-22 17:58:32
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 4
Author PrimeFan (13766)
Entry type Theorem
Classification msc 11N05