A062573 Numbers k such that 7^k - 6^k is prime.

2, 3, 7, 29, 41, 67, 1327, 1399, 2027, 69371, 86689, 355039

Offset: 1

Author

Mike Oakes, May 18 2001, May 19 2001

Keywords

• nonn
• hard

Comments

Terms greater than 1000 often correspond only to strong probable primes.

Examples

			7^2 - 6^2 = 49 - 36 = 13, which is prime, so 2 is in the sequence.
7^3 - 6^3 = 343 - 216 = 127, which is prime, so 3 is in the sequence.
		

Links

• Henri & Renaud Lifchitz, Top probable primes of the form 7^p-6^p

Crossrefs

Cf. A000043, A057468, A059801, A059802, A062572-A062666.

Programs

Mathematica

Select[Range[100], PrimeQ[7^# - 6^#] &] (* Alonso del Arte, Sep 04 2013 *)

PARI

is(n)=ispseudoprime(7^n-6^n) \\ Charles R Greathouse IV, Feb 20 2017

Extensions

Two more terms (69371 and 86689) found by Predrag Minovic in 2004 corresponding to probable primes with 58626 and 73261 digits. - Jean-Louis Charton, Oct 06 2010

New term 355039 found by Jean-Louis Charton in May 2011 corresponding to a probable prime with 300043 digits.