A Wagstaff prime is a prime number of the form (2^p + 1)/3 for p a prime number. The first few are given by p = 3, 5, 7, 11, 13, 17, 19, 23, 31, 43, 61, 79, 101, 127, 167, 191, 199, 313, 347, 701, 1709, 2617, 3539, 5807, 10501, 10691, 11279, 12391, 14479, 42737, 83339, 95369, 117239, 127031, 138937, 141079, 267017, 269987, 374321, 986191, and 4031399 (OEIS A000978), with p = 83339 and larger corresponding to probable primes. These values p correspond to the primes p_n with indices n = 2, 3, 4, 5, 6, 7, 8, 9, 11, 14, 18, 22, 26, ... (OEIS A123176). The Wagstaff primes are featured in the new Mersenne prime conjecture.
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