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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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1
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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; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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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LINKS
| Harvey P. Dale, Table of n, a(n) for n = 1..1000
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EXAMPLE
| 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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MATHEMATICA
| Select[Prime[Range[400]], PrimeQ[#^4+28642]&] (* From Harvey P. Dale, Dec 14 2011 *)
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PROG
| (MAGMA) [ p: p in PrimesUpTo(1840) | IsPrime(p^4+28642) ]; - Klaus Brockhaus
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CROSSREFS
| Cf. A158979, A159829, A160022.
Sequence in context: A020614 A191026 A158296 * A045427 A115165 A050583
Adjacent sequences: A160022 A160023 A160024 * A160026 A160027 A160028
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KEYWORD
| easy,nonn
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AUTHOR
| Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 30 2009
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EXTENSIONS
| Edited and extended beyond 857 by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 03 2009
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