A050266 Primes of the form n^3 + n^2 + 17, for nonnegative values of n.

17, 19, 29, 53, 97, 167, 269, 409, 593, 827, 1117, 1889, 2383, 2957, 3617, 6173, 7237, 9719, 11149, 12713, 16267, 18269, 25247, 27917, 33809, 47969, 56333, 65617, 70619, 75869, 81373, 99469, 112913, 120067, 143329, 151703, 160397, 188459

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• easy

Comments

n=-2 produces the prime 13. - Robert Price, Apr 25 2016

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Prime-Generating Polynomial.

Crossrefs

Cf. A331950.

Programs

Magma

[a: n in [0..100] | IsPrime(a) where a is  n^3+n^2+17]; // Vincenzo Librandi, Dec 08 2011

Maple

f:= seq(n^3+n^2+17, n = 0..100); select(isprime, f); # G. C. Greubel, Feb 06 2020

Mathematica

Select[Table[n^3+n^2+17,{n,0,100}],PrimeQ] (* Vincenzo Librandi, Dec 08 2011 *)

PARI

for(n=0, 100, my(m=n^3+n^2+17); if(isprime(m), print1(m ", "))) \\ G. C. Greubel, Feb 06 2020

Sage

[n^3+n^2+17 for n in (0..100) if is_prime(n^3+n^2+17) ] # G. C. Greubel, Feb 06 2020

Extensions

17 added by Vincenzo Librandi, Dec 08 2011

Altered definition to require that n be nonnegative. - Robert Price, Apr 25 2016