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Numbers k such that (4^k + 5^k)/9 is prime.
31

%I #18 Jul 10 2022 03:58:11

%S 5,7,19,29,61,137,883,1381,1823,5227,25561,29537,300893

%N Numbers k such that (4^k + 5^k)/9 is prime.

%C All terms are primes.

%H Henri Lifchitz and Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=%285%5Ep%2B4%5Ep%29%2F9">Top probable primes of the form (5^p+4^p)/9</a>

%t k=4; Do[p=Prime[n]; f=(k^p+5^p)/(k+5); If[ PrimeQ[f], Print[p] ], {n,1,100}]

%o (PARI) forprime(p=3,1e4,if(ispseudoprime((5^p+4^p)/9),print1(p", "))) \\ _Charles R Greathouse IV_, Jul 16 2011

%K hard,more,nonn

%O 1,1

%A _Alexander Adamchuk_, Feb 27 2007

%E 3 more terms from _Ryan Propper_, Feb 06 2008

%E Two more terms from _Ryan Propper_, May 02 2010

%E New term 300893 found by Jean-Louis Charton in November 2011 corresponding to a probable prime with 210315 digits.