A000979 Wagstaff primes: primes of form (2^p + 1)/3.

3, 11, 43, 683, 2731, 43691, 174763, 2796203, 715827883, 2932031007403, 768614336404564651, 201487636602438195784363, 845100400152152934331135470251, 56713727820156410577229101238628035243, 62357403192785191176690552862561408838653121833643

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Also, the primes with prime indices in the Jacobsthal sequence A001045.

Indices n such that (2^n + 1)/3 is prime are listed in A000978. - Alexander Adamchuk, Oct 03 2006

Primes in A126614. - Omar E. Pol, Nov 05 2013

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• T. D. Noe, Table of n, a(n) for n=1..20
• P. Berrizbeitia, F. Luca, and R. Melham, On a compositeness test for (2^p+1)/3, JIS 13 (2010) 10.1.7
• C. Caldwell's The Top Twenty, Wagstaff.
• Ernest G. Hibbs, Component Interactions of the Prime Numbers, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.
• Editor's Note, Table of Wagstaff primes sent by D. H. Lehmer, Math. Mag., 27 (1954), 156-157.
• Editor's Note, Table of Wagstaff primes sent by D. H. Lehmer (annotated and scanned copy)
• Djurre G. Sikkema, Probable primality testing for Wagstaff prime, Bachelor's project mathematics, Univ. Groningen (Netherlands 2024). See p. 32.
• S. S. Wagstaff, Jr., The Cunningham Project.
• Wikipedia, Wagstaff prime

Crossrefs

Cf. A000978, A049883, A001045, A127962.

Cf. A010051; subsequence of A007583.

Programs

Haskell

a000979 n = a000979_list !! (n-1)
a000979_list = filter ((== 1) . a010051) a007583_list
-- Reinhard Zumkeller, Mar 24 2013

Mathematica

Select[ Array[(2^# + 1)/3 &, 190], PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Apr 03 2010 *)

PARI

forprime(p=2,10000,if(ispseudoprime(2^p\/3),print1(2^p\/3,","))) \\ Edward Jiang, Sep 05 2014

Python

from gmpy2 import divexact
from sympy import prime, isprime
A000979 = [p for p in (divexact(2**prime(n)+1,3) for n in range(2,10**2)) if isprime(p)] # Chai Wah Wu, Sep 04 2014