A059802 Numbers k such that 5^k - 4^k is prime.

3, 43, 59, 191, 223, 349, 563, 709, 743, 1663, 5471, 17707, 19609, 35449, 36697, 45259, 91493, 246497, 265007, 289937

Offset: 1

Author

Mike Oakes, Feb 23 2001

Keywords

• nonn
• hard
• more

Comments

Some of the larger terms may only correspond to probable primes.

5^1663 - 4^1663, a 1163-digit number, has been certified prime with Primo. - Rick L. Shepherd, Nov 13 2002

4 more terms found by Predrag Minovic in 2004: 35449, 36697, 45259, 91493. Corresponding numbers of decimal digits are 24778, 25651, 31635, 63951. - Alexander Adamchuk, Dec 02 2006

Crossrefs

Cf. A005060.

Cf. A000043, A057468, A059801, A128335, etc.

Programs

Mathematica

Select[Range[1000], PrimeQ[5^# - 4^#] &] (* Alonso del Arte, Sep 09 2013 *)

PARI

forprime(p=2,1e5,if(ispseudoprime(5^p-4^p),print1(p", "))) \\ Charles R Greathouse IV, Jun 10 2011

Extensions

New term 246497 found by Jean-Louis Charton in 2008 corresponding to a probable prime with 172295 digits - Jean-Louis Charton, Sep 02 2009

New term a(19) = 265007 found by Jean-Louis Charton, Feb 19 2013

a(20) = 289937 found by Jean-Louis Charton, Mar 15 2013