%I #36 Aug 30 2021 04:05:12

%S 3,43,59,191,223,349,563,709,743,1663,5471,17707,19609,35449,36697,

%T 45259,91493,246497,265007,289937

%N Numbers k such that 5^k - 4^k is prime.

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

%C 5^1663 - 4^1663, a 1163-digit number, has been certified prime with Primo. - _Rick L. Shepherd_, Nov 13 2002

%C 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

%t Select[Range[1000], PrimeQ[5^# - 4^#] &] (* _Alonso del Arte_, Sep 09 2013 *)

%o (PARI) forprime(p=2,1e5,if(ispseudoprime(5^p-4^p),print1(p", "))) \\ _Charles R Greathouse IV_, Jun 10 2011

%Y Cf. A005060.

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

%K nonn,hard

%O 1,1

%A _Mike Oakes_, Feb 23 2001

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

%E New term a(19) = 265007 found by _Jean-Louis Charton_, Feb 19 2013

%E a(20) = 289937 found by _Jean-Louis Charton_, Mar 15 2013