%I #11 Apr 18 2023 18:44:13
%S 7,11,13,19,23,31,41,47,61,67,73,83,101,107,127,157,163,191,193,277,
%T 281,311,337,373,379,401,409,431,443,461,491,523,541,569,607,643,673,
%U 691,719,733,743,757,769,887,929,947,953,1031,1039,1087,1093,1097,1103,1109
%N Primes p such that p^4 + 11^4 + 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 = 11, r = 3.
%C It is conjectured that the sequence is infinite.
%C There are prime twins (11, 13) and other consecutive primes (7, 11; 1093, 1097) in the sequence.
%H Harvey P. Dale, <a href="/A160024/b160024.txt">Table of n, a(n) for n = 1..1000</a>
%e p = 3: 3^4 + 11^4 + 3^4 = 14803 = 113*131, so 3 is not in the sequence.
%e p = 7: 7^4 + 11^4 + 3^4 = 17123 is prime, so 7 is in the sequence.
%e p = 11: 11^4 + 11^4 + 3^4 = 29363 is prime, so 11 is in the sequence.
%e p = 13: 13^4 + 11^4 + 3^4 = 43283 is prime, so 13 is in the sequence.
%t Select[Prime[Range[200]],PrimeQ[#^4+14722]&] (* _Harvey P. Dale_, Apr 18 2023 *)
%o (Magma) [ p: p in PrimesUpTo(1110) | IsPrime(p^4+14722) ]; // _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 and extended beyond 461 by _Klaus Brockhaus_, May 03 2009