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A160023
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Primes p such that p^4+7^4+3^4 is prime.
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0
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11, 37, 71, 101, 149, 163, 191, 271, 293, 379, 409, 419, 647, 661, 709, 1153, 1193, 1231, 1277, 1523, 1583, 1619, 1667, 1693, 1753, 1777, 1787, 1913, 2089, 2099, 2161, 2213, 2441, 2473, 2531, 2551, 2609, 2711, 2749, 2909, 2953, 2999, 3221, 3257, 3469
(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 = 7, r = 3.
It is conjectured that the sequence is infinite.
There are prime twins (6197, 6199) and other consecutive primes (409, 419; 2089, 2099) in the sequence.
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EXAMPLE
| p = 7: 7^4+7^4+3^4 = 4883 = 19*257, so 7 is not in the sequence.
p = 11: 11^4+7^4+3^4 = 17123 is prime, so 11 is in the sequence.
p = 101: 101^4+7^4+3^4 = 104062883 is prime, so 101 is in the sequence.
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PROG
| (MAGMA) [ p: p in PrimesUpTo(3500) | IsPrime(p^4+2482) ]; - Klaus Brockhaus
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CROSSREFS
| Cf. A158979, A159829, A160022.
Sequence in context: A099227 A122728 A031381 * A188135 A188382 A090950
Adjacent sequences: A160020 A160021 A160022 * A160024 A160025 A160026
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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 2441 by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 03 2009
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