A195905 Primes of the form 10 * n^2 + 7.

7, 17, 47, 97, 167, 257, 367, 647, 1217, 1447, 1697, 2897, 3617, 4007, 5297, 6257, 7297, 9007, 10247, 12967, 13697, 14447, 15217, 16007, 26017, 28097, 29167, 32497, 33647, 36007, 37217, 38447, 42257

Offset

1,1

Comments

First seven numbers of the form 10 * n^2 + 7 are prime numbers. They are called Trotter primes by Terrel Trotter Jr. There are 735 Trotter primes less than 10^8.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

T. Trotter, Trotter numbers and Trotter primes [Warning: As of March 2018 this site appears to have been hacked. Proceed with great caution. The original content should be retrieved from the Wayback machine and added here. - N. J. A. Sloane, Mar 29 2018]

Mathematica

Select[Table[10n^2+7, {n, 0, 500}], PrimeQ] (* Vincenzo Librandi, Dec 04 2011 *)
Select[(10*Range[0, 70]^2+7), PrimeQ] (* Harvey P. Dale, Dec 11 2018 *)

Prog

(Magma) [a: n in [0..300] | IsPrime(a) where a is 10*n^2+7]; // Vincenzo Librandi, Dec 05 2011

Crossrefs

Cf. A000040, A061722.

Sequence in context: A179031 A107178 A061722 * A104164 A192244 A110097

Adjacent sequences: A195902 A195903 A195904 * A195906 A195907 A195908

Keyword

nonn,easy

Author

Kausthub Gudipati, Sep 25 2011

Extensions

7 inserted by Omar E. Pol, Oct 03 2011

Restored the primitive offset by Vincenzo Librandi, Dec 04 2011

Status

approved