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Search: id:A160025
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| A160025 |
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Primes p such that p^4+13^4+3^4 is prime. |
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| 3, 11, 13, 17, 31, 41, 43, 53, 83, 127, 167, 181, 193, 211, 241, 311, 337, 349, 421, 431, 487, 521, 557, 613, 617, 647, 701, 769, 811, 857, 953, 1021, 1151, 1249, 1289, 1303, 1373, 1453, 1459, 1471, 1523, 1553, 1567, 1579, 1613, 1663, 1669, 1747, 1823, 1831
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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 = 13, r = 3.
It is conjectured that the sequence is infinite.
There are prime twins (11, 13) and other consecutive primes (421, 431; 1823, 1831) in the sequence.
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EXAMPLE
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p = 3: 3^4+13^4+3^4 = 28723 is prime, so 3 is in the sequence.
p = 5: 5^4+13^4+3^4 = 29267 = 7*37*113, so 5 is not in the sequence.
p = 17: 17^4+13^4+3^4 = 112163 is prime, so 17 is in the sequence.
p = 83: 83^4+13^4+3^4 = 47486963 is prime, so 83 is in the sequence.
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PROGRAM
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(MAGMA) [ p: p in PrimesUpTo(1840) | IsPrime(p^4+28642) ]; - Klaus Brockhaus
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CROSSREFS
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Cf. A158979, A159829, A160022.
Sequence in context: A045426 A020614 A158296 this_sequence A045427 A115165 A050583
Adjacent sequences: A160022 A160023 A160024 this_sequence A160026 A160027 A160028
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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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Edited and extended beyond 857 by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 03 2009
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