A065509 Primes p such that p^4 + p^3 + p^2 + p + 1 is prime.

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

Offset: 1

Author

Vladeta Jovovic, Nov 26 2001

Keywords

• easy
• nonn

Comments

Primes in A049409. - Vincenzo Librandi, Aug 07 2010

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

Examples

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

Links

• Jon E. Schoenfield, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harry J. Smith).

Crossrefs

Cf. A053182.

Programs

Magma

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

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 *)

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

PARI

{A065509_vec(N,p=1)=vector(N,i,until(isprime((p^5-1)\(p-1)),p=nextprime(p+1));p)} \\ M. F. Hasler, Mar 03 2020