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
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.
^Bateman, P. T.; Selfridge, J. L.; Wagstaff, Jr., S. S. (1989). "The New Mersenne Conjecture". American Mathematical Monthly. 96: 125–128. doi:10.2307/2323195. JSTOR 2323195.
theory, a Wagstaffprime is a prime number of the form 2 p + 1 3 {\displaystyle {{2^{p}+1} \over 3}} where p is an odd prime. Wagstaffprimes are named...
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television series Bob's Burgers Wagstaffprime, in number theory Alfred Wagstaff Jr. (1844–1921), New York politician Barry Wagstaff (born 1945), English association...
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number k. (OEIS: A122834) 2p − 1 is prime (a Mersenne prime). (OEIS: A000043) (2p + 1)/3 is prime (a Wagstaffprime). (OEIS: A000978) If p is an odd composite...
Newman–Shanks–Williams prime Primorial primeWagstaffprime Wall–Sun–Sun prime Wieferich prime Wilson prime Wolstenholme prime Woodall primePrime pages Covering...
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several manuals of computer graphics), and Samuel S. Wagstaff Jr. (inventor of the Wagstaffprime). Purdue's tenured faculty comprises sixty Academic Deans...
of Mersenne primes is the subject of the Lenstra–Pomerance–Wagstaff conjecture, which states that the expected number of Mersenne primes less than some...
have been married to the British prime minister in office. There have also been four bachelor and nine widower prime ministers; the last bachelor was...
Richard Wagstaff Clark (November 30, 1929 – April 18, 2012) was an American television and radio personality and television producer who hosted American...
1997. ISBN 0-201-89684-2. Section 4.5.4: Factoring into Primes, pp. 379–417. Samuel S. Wagstaff Jr. (2013). The Joy of Factoring. Providence, RI: American...
is prime. Among other fields of mathematics, it is used for cryptography. Unlike integer factorization, primality tests do not generally give prime factors...
In number theory, a Wieferich prime is a prime number p such that p2 divides 2p − 1 − 1, therefore connecting these primes with Fermat's little theorem...
618970019642690137449562111, ... 2p − 1 is prime, where p is a prime. A000668 Wagstaffprimes 3, 11, 43, 683, 2731, 43691, ... A prime number p of the form p = 2 q...
If 2k + 1 is prime and k > 0, then k itself must be a power of 2, so 2k + 1 is a Fermat number; such primes are called Fermat primes. As of 2023[update]...
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