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A160022 Primes p such that p^4 + 5^4 + 3^4 is prime. 6
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; text; internal format)
OFFSET

1,1

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 twin prime (101, 103) and other consecutive primes (151, 157; 1867, 1871) in the sequence.

LINKS

Table of n, a(n) for n=1..47.

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.

MATHEMATICA

With[{c=5^4+3^4}, Select[Prime[Range[600]], PrimeQ[#^4+c]&]] (* Harvey P. Dale, Aug 14 2011 *)

PROG

(MAGMA) [p: p in PrimesUpTo(5000)|IsPrime(p^4+706)] // Vincenzo Librandi, Dec 18 2010

(PARI) is(n)=isprime(n) && isprime(n^4+706) \\ Charles R Greathouse IV, Jun 07 2016

CROSSREFS

Cf. A158979, A159829, A160031.

Sequence in context: A014582 A146142 A105854 * A307530 A187094 A060651

Adjacent sequences:  A160019 A160020 A160021 * A160023 A160024 A160025

KEYWORD

easy,nonn

AUTHOR

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 30 2009

EXTENSIONS

Edited, 1607 inserted and extended beyond 3643 by Klaus Brockhaus, May 03 2009

STATUS

approved

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Last modified May 19 10:36 EDT 2019. Contains 323390 sequences. (Running on oeis4.)