Wagstaff prime

Wagstaff prime

Named after	Samuel S. Wagstaff, Jr.
Publication year	1989[1]
Author of publication	Bateman, P. T., Selfridge, J. L., Wagstaff Jr., S. S.
No. of known terms	44
First terms	3, 11, 43, 683
Largest known term	(2138937+1)/3
OEIS index	A000979 Wagstaff primes: primes of form (2^p + 1)/3

In number theory, a Wagstaff prime is a prime number of the form

${\displaystyle {{2^{p}+1} \over 3}}$

where p is an odd prime. Wagstaff primes are named after the mathematician Samuel S. Wagstaff Jr.; the prime pages credit François Morain for naming them in a lecture at the Eurocrypt 1990 conference. Wagstaff primes appear in the New Mersenne conjecture and have applications in cryptography.