A128336 Numbers k such that (6^k + 5^k)/11 is prime.

3, 5, 17, 397, 409, 643, 1783, 2617, 4583, 8783

Offset: 1

Author

Alexander Adamchuk, Feb 27 2007

Keywords

• hard
• more
• nonn

Comments

All terms are primes.

No other terms less than 100000. - Robert Price, May 11 2012

Crossrefs

Cf. A057171, A082387, A122853, A128335, A128337, A128338, A128339, A128340, A128341, A128342, A128343, A004061, A082182, A121877, A059802, A062572, A128344, A128345, A128346, A128347, A128348, A128349, A128350, A128351, A128352, A128353, A128354.

Programs

Mathematica

k=6; 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((6^p+5^p)/11),print1(p", "))) \\ Charles R Greathouse IV, Jul 16 2011

Extensions

a(7)-a(9) from Alexander Adamchuk, May 04 2010

One more term (8783) added (unknown discoverer) corresponding to a probable prime with 6834 digits by Jean-Louis Charton, Oct 06 2010