A289839 Primes of the form 8*n^2+8*n+31.

31, 47, 79, 127, 191, 271, 367, 479, 607, 751, 911, 1087, 1279, 1487, 1951, 2207, 2767, 3391, 3727, 4079, 4447, 4831, 5231, 5647, 6079, 6991, 9007, 9551, 10111, 10687, 11279, 11887, 12511, 13151, 13807, 14479, 17327, 20431, 21247, 22079, 24671, 26479, 27407

Offset: 1

Author

Waldemar Puszkarz, Oct 06 2017

Keywords

• nonn

Comments

The first 14 terms correspond to n from 0 to 13, which makes 8*n^2+8*n+31 a prime-generating polynomial (see the link).

This is a prime-generating polynomial of the form c*n^2+c*n+p, where c=2^k (k=0,1,2...) and p is prime with c and p containing at most two digits. Prime-generating polynomials of this kind arise for k=0,1,2,3 - see A005846 and A007635 (k=0), A007639 (k=1), and A048988 (k=2).

All terms are of the form 4m+3. Terms 1 and 4 are Mersenne primes (A000668).

Examples

			79 is a term as it is a prime corresponding to n=2: 8*4+8*2+31=79.
		

Links

• Eric Weisstein's World of Mathematics, Prime-Generating Polynomial

Crossrefs

Cf. A000040 (primes), A005846, A007635, A007639, A048988, A281437, A292578 (similar prime-generating sequences).

Programs

Mathematica

Select[Range[0,100]//8#^2+8#+31&, PrimeQ]

PARI

for(n=0, 100, isprime(p=8*n^2+8*n+31)&& print1(p ", "))