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A158361
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Primes p with property that Q=p^4+2^4 is prime
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1
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3, 5, 7, 11, 17, 19, 23, 37, 41, 59, 61, 71, 79, 97, 131, 139, 179, 223, 227, 229, 241, 283, 313, 317, 359, 367, 379, 383, 389, 439, 449, 461, 487, 503, 521, 569, 593, 617, 619, 631, 661, 683, 709, 733, 811, 821, 853, 911, 977, 1049, 1061, 1063, 1069, 1091, 1093, 1117
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Q is always congruent to 1 (mod 4)
Q is divisible by 17 if p is congruent to 1, 4, 13, or 16 (mod 17)
It is conjectured that sequence a(n) is infinite
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REFERENCES
| Leonard E. Dickson, History of the Theory of numbers, vol. I, Dover Publications 2005
Richard Guy, "Unsolved Problems in Number Theory"
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EXAMPLE
| 3 is in the sequence since for p=3: p^4+2^4 = 3^4+16 = 97 is prime
29 is not in the sequence since 29^4+2^4 = 707297 = 73 x 9689 is not prime
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PROG
| (PARI) isA158361(n) = isprime(n) && isprime(n^4+16)
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CROSSREFS
| Cf. A062324 A157950 A157764.
Sequence in context: A085498 A128926 A139559 * A048184 A163420 A155489
Adjacent sequences: A158358 A158359 A158360 * A158362 A158363 A158364
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KEYWORD
| nonn
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AUTHOR
| Ulrich Krug (leuchtfeuer37(AT)gmx.de), Mar 17 2009
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EXTENSIONS
| Corrected and edited by Michael Porter (michael_b_porter(AT)yahoo.com), Dec 17 2009
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