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%I #7 Sep 08 2022 08:45:44
%S 13,29,37,59,89,101,107,241,263,293,373,409,569,683,821,971,1033,1187,
%T 1229,1277,1289,1423,1511,1627,1759,1823,1901,1907,1973,2011,2069,
%U 2083,2099,2207,2311,2473,2593,2633,2707,2719,2753,2819,3023,3137,3209,3221
%N Primes p such that p^4 + 17^4 + 3^4 is prime.
%C For primes p, q, r the sum p^4 + q^4 + r^4 can be prime only if at least one of p, q, r equals 3. This sequence is the special case q = 17, r = 3.
%C It is conjectured that the sequence is infinite.
%C There are consecutive primes (1901, 1907) in the sequence.
%e p = 3: 3^4 + 17^4 + 3^4 = 83683 = 67*1249, so 3 is not in the sequence.
%e p = 1901: 1901^4 + 17^4 + 3^4 = 13059557751203 is prime, so 1901 is in the sequence.
%e p = 1907: 1907^4 + 17^4 + 3^4 = 13225216032803 is prime, so 1907 is in the sequence.
%o (Magma) [ p: p in PrimesUpTo(3250) | IsPrime(p^4+83602) ]; // _Klaus Brockhaus_, May 03 2009
%Y Cf. A158979, A159829, A160022.
%K easy,nonn
%O 1,1
%A Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 30 2009
%E Edited, 409 inserted and extended beyond 2069 by _Klaus Brockhaus_, May 03 2009
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