A006034 Numbers n such that (17^n-1)/16 is prime.

3, 5, 7, 11, 47, 71, 419, 4799, 35149, 54919, 74509, 1990523

Offset: 1

Author

N. J. A. Sloane

Keywords

• hard
• nonn
• more

Comments

No others for any n less than 8447. - Julien Peter Benney (jpbenney(AT)ftml.net), Aug 15 2004

References

• Ribenboim, Paulo; "The Book Of Prime Number Records"; published 1989 by Springer-Verlag; pages 350-354.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• 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

Programs

Mathematica

lst={};Do[If[PrimeQ[(17^n-1)/16], Print[n];AppendTo[lst, n]], {n, 10^5}];lst (* Vladimir Joseph Stephan Orlovsky, Aug 21 2008 *)

PARI

is(n)=isprime((17^n-1)/16) \\ Charles R Greathouse IV, Apr 28 2015

Extensions

a(9)=35149 & a(10)=54919 are probable primes discovered by Paul Bourdelais, Mar 08 2010

a(11)=74509 is a probable prime discovered by Paul Bourdelais, Mar 10 2010

a(12)=1990523 corresponds to a probable prime discovered by Paul Bourdelais, Aug 03 2020