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%I #11 Sep 08 2022 08:45:44
%S 11,37,71,101,149,163,191,271,293,379,409,419,647,661,709,1153,1193,
%T 1231,1277,1523,1583,1619,1667,1693,1753,1777,1787,1913,2089,2099,
%U 2161,2213,2441,2473,2531,2551,2609,2711,2749,2909,2953,2999,3221,3257,3469
%N Primes p such that p^4 + 7^4 + 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 = 7, r = 3.
%C It is conjectured that the sequence is infinite.
%C There are prime twins (6197, 6199) and other consecutive primes (409, 419; 2089, 2099) in the sequence.
%H Harvey P. Dale, <a href="/A160023/b160023.txt">Table of n, a(n) for n = 1..1000</a>
%e p = 7: 7^4 + 7^4 + 3^4 = 4883 = 19*257, so 7 is not in the sequence.
%e p = 11: 11^4 + 7^4 + 3^4 = 17123 is prime, so 11 is in the sequence.
%e p = 101: 101^4 + 7^4 + 3^4 = 104062883 is prime, so 101 is in the sequence.
%t Select[Prime[Range[500]],PrimeQ[#^4+2482]&] (* _Harvey P. Dale_, Jan 31 2017 *)
%o (Magma) [ p: p in PrimesUpTo(3500) | IsPrime(p^4+2482) ]; // _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 2441 by _Klaus Brockhaus_, May 03 2009