A128878 Primes of the form 47*n^2 - 1701*n + 10181.

10181, 8527, 6967, 5501, 4129, 2851, 1667, 577, 379, 1451, 2617, 3877, 5231, 6679, 8221, 9857, 11587, 13411, 15329, 17341, 19447, 21647, 31387, 34057, 36821, 39679, 45677, 48817, 52051, 65927, 81307, 89561, 102647, 107197, 116579, 126337, 131357

Offset: 1

Author

Douglas Winston (douglas.winston(AT)srupc.com), Apr 17 2007

Keywords

• nonn

Comments

Primes are given in the order in which they arise for increasing n.

Polynomial generates 22 primes for 0 <= n <= 42, i.e., for n = 0, 1, 2, 3, 4, 5, 6, 7, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42.

If the definition is replaced by "Numbers n of the form 47*k^2 - 1701*k + 10181 such that either n or -n is a prime" we get (essentially) A050267.

Examples

			47k^2 - 1701k + 10181 = 21647 for k = 42.
		

References

• R. K. Guy, Unsolved Problems in Number Theory, 3rd edition, Springer, 2004, ISBN 0-387-20860-7, Section A17, page 59.

Links

• G. W. Fung and H. C. Williams, Quadratic polynomials which have a high density of prime values, Math. Comput. 55(191) (1990), 345-353.
• Carlos Rivera, Problem 12: Prime producing polynomials, The Prime Puzzles and Problems Connection.

Crossrefs

Cf. A050267, A002383, A027753, A027755, A005471, A027758, A048059, A007635, A005846, A116206, A050268, A022464.

Programs

Mathematica

Select[Table[47*n^2 - 1701*n + 10181, {n, 0, 100}], # > 0 && PrimeQ[#] &] (* T. D. Noe, Aug 02 2011 *)

Extensions

Edited by Klaus Brockhaus, Apr 22 2007 and by N. J. A. Sloane, May 05 2007 and May 06 2007