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.
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
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