A Wagstaff prime is a prime of the form \((2^p + 1)/3\), where \(p\) is an odd prime. The sequence: 3, 11, 43, 683, 2731, 43691, 174763, 2796203, 715827883.
They are the "new Mersenne" cousins — closely tied to the [[mersenne-prime]]s through the New Mersenne Conjecture of Bateman, Selfridge, and Wagstaff. Like Mersenne primes, the large ones are found by distributed search; they also appear in the study of repunits in base −2. Named after Samuel Wagstaff.