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A065509 Primes p such that p^4 + p^3 + p^2 + p + 1 is prime. 6
2, 7, 13, 17, 23, 29, 43, 73, 79, 83, 127, 193, 227, 239, 263, 277, 337, 359, 373, 397, 439, 457, 479, 503, 557, 563, 617, 919, 967, 1009, 1129, 1187, 1249, 1297, 1327, 1429, 1493, 1553, 1579, 1657, 1663, 1979, 1987, 2069, 2243, 2383, 2617, 2663, 2789 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Primes in A049409. [Vincenzo Librandi, Aug 07 2010]

The generated prime numbers are in A190527. [Bernard Schott, Dec 20 2012]

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

EXAMPLE

a(4)=17 because 17 is prime and 17^4 + 17^3 + 17^2 + 17 + 1 = 88741 is prime.

MATHEMATICA

f[n_]:=1+n+n^2+n^3+n^4; lst={}; Do[p=Prime[n]; If[PrimeQ[f[p]], AppendTo[lst, p]], {n, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 24 2009 *)

Select[Prime[Range[500]], PrimeQ[Total[#^Range[0, 4]]]&] (* Harvey P. Dale, Apr 08 2017 *)

PROG

(PARI) { n=0; for (m=1, 10^9, p=prime(m); if (isprime(p^4 + p^3 + p^2 + p + 1), write("b065509.txt", n++, " ", p); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 20 2009

(MAGMA) [n: n in [0..10000]| IsPrime(n) and IsPrime(n^4+n^3+n^2+n+1)] // Vincenzo Librandi, Aug 07 2010

CROSSREFS

Cf. A053182.

Sequence in context: A250185 A063206 A063099 * A094516 A105883 A191036

Adjacent sequences:  A065506 A065507 A065508 * A065510 A065511 A065512

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Nov 26 2001

STATUS

approved

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Last modified October 23 14:45 EDT 2019. Contains 328345 sequences. (Running on oeis4.)