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%I #11 Sep 08 2022 08:45:44
%S 5,13,19,43,71,83,97,101,107,109,127,149,179,193,197,211,233,241,311,
%T 353,383,401,421,541,577,599,607,619,641,647,683,709,727,751,769,827,
%U 877,883,941,967,991,1009,1061,1097,1109,1187,1289,1373,1381,1409,1439
%N Primes p such that p^4 + 2*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 = r = 3.
%C It is conjectured that the sequence is infinite.
%C There are prime twins (107, 109) and other consecutive primes (193, 197) in the sequence.
%H Harvey P. Dale, <a href="/A160031/b160031.txt">Table of n, a(n) for n = 1..1000</a>
%e p = 5: 5^4 + 2*3^4 = 787 is prime, so 5 is in the sequence.
%e p = 7: 7^4 + 2*3^4 = 2563 = 11*233, so 7 is not in the sequence.
%e p = 107: 107^4 + 2*3^4 = 131079763 is prime, so 107 is in the sequence.
%e p = 109: 109^4 + 2*3^4 = 141158323 is prime, so 109 is in the sequence.
%t Select[Prime[Range[300]],PrimeQ[#^4+162]&] (* _Harvey P. Dale_, May 10 2018 *)
%o (Magma) [ p: p in PrimesUpTo(1450) | IsPrime(p^4+162) ]; // _Klaus Brockhaus_, May 03 2009
%o (PARI) is(n)=isprime(n) && isprime(n^4+162) \\ _Charles R Greathouse IV_, Jun 07 2016
%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 683 by _Klaus Brockhaus_, May 03 2009