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A160022
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Primes p such that p^4+5^4+3^4 is prime.
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6
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3, 23, 47, 53, 67, 73, 89, 101, 103, 109, 151, 157, 179, 229, 521, 557, 569, 619, 661, 821, 977, 1013, 1087, 1129, 1277, 1321, 1451, 1559, 1607, 1627, 1741, 1867, 1871, 1949, 2137, 2389, 2441, 2797, 3271, 3313, 3643, 3677, 3769, 3847, 4001, 4027, 4133
(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 = 5, r = 3.
It is conjectured that the sequence is infinite.
There are prime twins (101, 103) and other consecutive primes (151, 157; 1867, 1871) in the sequence.
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EXAMPLE
| p = 3: 3^4+5^4+3^4 = 787 is prime, so 3 is in the sequence.
p = 5: 5^4+5^4+3^4 = 1331 = 11^3, so 5 is not in the sequence.
p = 101: 101^4+5^4+3^4 = 104061107 is prime, so 101 is in the sequence.
p = 103: 103^4+5^4+3^4 = 112551587 is prime, so 103 is in the sequence.
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MATHEMATICA
| With[{c=5^4+3^4}, Select[Prime[Range[600]], PrimeQ[#^4+c]&]] (* From Harvey P. Dale, Aug 14 2011 *)
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PROG
| (MAGMA)[p: p in PrimesUpTo(5000)|IsPrime(p^4+706)][From Vincenzo Librandi, Dec 18 2010]
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CROSSREFS
| A158979, A159829, A160031.
Sequence in context: A014582 A146142 A105854 * A187094 A060651 A146592
Adjacent sequences: A160019 A160020 A160021 * A160023 A160024 A160025
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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, 1607 inserted and extended beyond 3643 by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 03 2009
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