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A160031
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Primes p such that p^4 + 2*3^4 is prime.
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2
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5, 13, 19, 43, 71, 83, 97, 101, 107, 109, 127, 149, 179, 193, 197, 211, 233, 241, 311, 353, 383, 401, 421, 541, 577, 599, 607, 619, 641, 647, 683, 709, 727, 751, 769, 827, 877, 883, 941, 967, 991, 1009, 1061, 1097, 1109, 1187, 1289, 1373, 1381, 1409, 1439
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OFFSET
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1,1
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COMMENTS
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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.
It is conjectured that the sequence is infinite.
There are prime twins (107, 109) and other consecutive primes (193, 197) in the sequence.
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LINKS
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EXAMPLE
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p = 5: 5^4 + 2*3^4 = 787 is prime, so 5 is in the sequence.
p = 7: 7^4 + 2*3^4 = 2563 = 11*233, so 7 is not in the sequence.
p = 107: 107^4 + 2*3^4 = 131079763 is prime, so 107 is in the sequence.
p = 109: 109^4 + 2*3^4 = 141158323 is prime, so 109 is in the sequence.
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MATHEMATICA
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Select[Prime[Range[300]], PrimeQ[#^4+162]&] (* Harvey P. Dale, May 10 2018 *)
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PROG
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(Magma) [ p: p in PrimesUpTo(1450) | IsPrime(p^4+162) ]; // Klaus Brockhaus, May 03 2009
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 30 2009
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EXTENSIONS
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STATUS
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approved
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