A004063 Numbers k such that (7^k - 1)/6 is prime.

5, 13, 131, 149, 1699, 14221, 35201, 126037, 371669, 1264699

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• hard
• more

Comments

Base-7 repunit primes. - Paul Bourdelais, Aug 31 2007

Among repunits with bases from -11 to 11, base-7 repunits have the lowest relative rate of occurrence of primes so far. - Paul Bourdelais, Feb 23 2010

References

• J. Brillhart et al., Factorizations of b^n +- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 2nd edition, 1985; and later supplements.
• Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 236.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Paul Bourdelais, A Generalized Repunit Conjecture
• J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
• H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927-930.
• H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927-930. [Annotated scanned copy]
• H. Lifchitz, Mersenne and Fermat primes field
• S. S. Wagstaff, Jr., The Cunningham Project
• Eric Weisstein's World of Mathematics, Repunit

Programs

Mathematica

For[n = 1, n <= 20000, n++, If[PrimeQ[(7^n - 1)/6 ], Print[n]]] (* Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 09 2006 *)

PARI

is(n)=isprime((7^n - 1)/6) \\ Charles R Greathouse IV, Apr 28 2015

Prime95

PRP=1,7,1264699,-1,0,0,"6"

Extensions

a(6) from Robert G. Wilson v, Apr 09 2005

a(7) is a probable prime from Paul Bourdelais, Aug 31 2007

a(8) discovered Sep 17 2008 by Paul Bourdelais & Eric Purohit - it is a probable prime based on trial factoring to 2.5*10^13 and Fermat base 2 primality test. - Paul Bourdelais, Sep 18 2008

a(9) is a probable prime discovered by Paul Bourdelais, Feb 23 2010

a(10) is a probable prime discovered by Paul Bourdelais, Jan 06 2014