Wagstaff Prime

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In number theory, a Wagstaff prime is a prime number p of the form p={{2^q+1}over 3} where q is another prime. Wagstaff primes are named after mathematician Samuel S. Wagstaff Jr., the prime pages credit François Morain for naming them in a lecture at the Eurocrypt 1990 conference. Wagstaff primes are related to the New Mersenne conjecture and have applications in cryptology.The first three Wagstaff primes are 3, 11, and 43 because begin{align} 3 & = {2^3+1 over 3}, [5pt] 11 & = {2^5+1 over 3}, [5pt] 43 & = {2^7+1 over 3}. end.The first few Wagstaff primes are: 3, 11, 43, 683, 2731, 43691, 174763, 2796203, 715827883, 2932031007403, (sequence A000979 in OEIS).The first exponents q which produce Wagstaff primes or probable primes are: 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, 4031399, (sequence A000978 in OEIS)