A062572 Numbers k such that 6^k - 5^k is prime.

2, 5, 11, 13, 23, 61, 83, 421, 1039, 1511, 31237, 60413, 113177, 135647, 258413

Offset: 1

Author

Mike Oakes, May 18 2001, May 19 2001

Keywords

• nonn
• hard
• more

Comments

The 809- and 1176-digit numbers associated with the terms 1039 and 1511 have been certified prime with Primo. - Rick L. Shepherd, Nov 15 2002

Examples

			2 is in the sequence because 6^2 - 5^2 = 36 - 25 = 11, which is prime.
3 is not in the sequence because 6^3 - 5^3 = 216 - 125 = 91 = 7 * 13, which is not prime.
		

Crossrefs

Cf. A000043, A057468, A059801, A059802, A062573-A062666.

Programs

Mathematica

Select[Range[1000], PrimeQ[6^# - 5^#] &] (* Alonso del Arte, Sep 04 2013 *)

PARI

forprime(p=2,1e4,if(ispseudoprime(6^n-5^n),print1(p", "))) \\ Charles R Greathouse IV, Jun 10 2011

Extensions

Edited by T. D. Noe, Oct 30 2008

Two more terms (31237 and 60413) found by Predrag Minovic in 2004 corresponding to probable primes with 24308 and 47011 digits. Jean-Louis Charton, Oct 06 2010

Two more terms (113177 and 135647) found by Jean-Louis Charton in 2009 corresponding to probable primes with 88069 and 105554 digits. Jean-Louis Charton, Oct 13 2010

a(15) from Jean-Louis Charton, Apr 08 2013