A128335 Numbers k such that (4^k + 5^k)/9 is prime.

5, 7, 19, 29, 61, 137, 883, 1381, 1823, 5227, 25561, 29537, 300893

Offset: 1

Author

Alexander Adamchuk, Feb 27 2007

Keywords

• hard
• more
• nonn

Comments

All terms are primes.

Links

• Henri Lifchitz and Renaud Lifchitz, Top probable primes of the form (5^p+4^p)/9

Programs

Mathematica

k=4; Do[p=Prime[n]; f=(k^p+5^p)/(k+5); If[ PrimeQ[f], Print[p] ], {n,1,100}]

PARI

forprime(p=3,1e4,if(ispseudoprime((5^p+4^p)/9),print1(p", "))) \\ Charles R Greathouse IV, Jul 16 2011

Extensions

3 more terms from Ryan Propper, Feb 06 2008

Two more terms from Ryan Propper, May 02 2010

New term 300893 found by Jean-Louis Charton in November 2011 corresponding to a probable prime with 210315 digits.