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Numbers k such that 8^k - 7^k is prime or a strong pseudoprime.
4

%I #29 Jul 04 2021 07:52:16

%S 7,11,17,29,31,79,113,131,139,4357,44029,76213,83663,173687,336419,

%T 615997

%N Numbers k such that 8^k - 7^k is prime or a strong pseudoprime.

%C All terms are prime. - _Alexander Adamchuk_, Apr 27 2008

%H Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=8%5Ex-7%5Ex&amp;action=Search">PRP Records</a>.

%t Select[Range[200], PrimeQ[8^# - 7^#] &] (* _Vladimir Joseph Stephan Orlovsky_, Feb 22 2012 *)

%o (PARI) is(n)=ispseudoprime(8^n-7^n) \\ _Charles R Greathouse IV_, Sep 04 2013

%Y Cf. A000043, A057468, A059801, A059802, A059803 (9^n-8^n is prime), A062572-A062666.

%Y Cf. A016177 = 8^n - 7^n.

%K nonn,hard

%O 1,1

%A _Mike Oakes_, May 18 2001, May 19 2001

%E Two more terms 44029 and 76213 found by Ananda Tallur & _Jean-Louis Charton_ in 2003.

%E Three more terms 83663, 173687 and 336419 found by _Jean-Louis Charton_ in 2004 and 2008

%E New term 615997 found by Jean-Louis Charton corresponding to a probable prime with 556301 digits. _Jean-Louis Charton_, Sep 02 2009