cp's OEIS Frontend

A160025 Primes p such that p^4 + 13^4 + 3^4 is prime.

%I A160025 #10 Sep 08 2022 08:45:44
%S A160025 3,11,13,17,31,41,43,53,83,127,167,181,193,211,241,311,337,349,421,
%T A160025 431,487,521,557,613,617,647,701,769,811,857,953,1021,1151,1249,1289,
%U A160025 1303,1373,1453,1459,1471,1523,1553,1567,1579,1613,1663,1669,1747,1823,1831
%N A160025 Primes p such that p^4 + 13^4 + 3^4 is prime.
%C A160025 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 = 13, r = 3.
%C A160025 It is conjectured that the sequence is infinite.
%C A160025 There are prime twins (11, 13) and other consecutive primes (421, 431; 1823, 1831) in the sequence.
%H A160025 Harvey P. Dale, <a href="/A160025/b160025.txt">Table of n, a(n) for n = 1..1000</a>
%e A160025 p = 3: 3^4 + 13^4 + 3^4 = 28723 is prime, so 3 is in the sequence.
%e A160025 p = 5: 5^4 + 13^4 + 3^4 = 29267 = 7*37*113, so 5 is not in the sequence.
%e A160025 p = 17: 17^4 + 13^4 + 3^4 = 112163 is prime, so 17 is in the sequence.
%e A160025 p = 83: 83^4 + 13^4 + 3^4 = 47486963 is prime, so 83 is in the sequence.
%t A160025 Select[Prime[Range[400]],PrimeQ[#^4+28642]&] (* _Harvey P. Dale_, Dec 14 2011 *)
%o A160025 (Magma) [ p: p in PrimesUpTo(1840) | IsPrime(p^4+28642) ]; // _Klaus Brockhaus_, May 03 2009
%Y A160025 Cf. A158979, A159829, A160022.
%K A160025 easy,nonn
%O A160025 1,1
%A A160025 Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 30 2009
%E A160025 Edited and extended beyond 857 by _Klaus Brockhaus_, May 03 2009