A117091 Primes of the form f(n) = n^6 - 48*n^5 + 908*n^4 - 8603*n^3 + 42796*n^2 - 105410*n + 100823 listed by increasing value of n >= 0.

100823, 30467, 5419, 89, 719, 1423, 947, 149, 199, 1499, 3323, 4177, 2879, 359, 2179, 21773, 84407, 231859, 527819, 1967023, 13443239, 19869323, 55748639, 75716119, 101253923, 173883799, 285153899, 449885327, 557975279, 686780659, 1475059259, 1759928369

Offset

1,1

Comments

This polynomial f(n) generates 19 prime numbers consecutively (for n=0 to n=18). In n^2 + n + 17, substitute n -> n^3 - 24*n^2 + 166*n - 318.

The polynomial f(n) generates 10790 primes in the first 100000 values. - Stefan Steinerberger, Apr 21 2006

References

Paulo Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 2nd ed., 1989, p. 137.

Links

Table of n, a(n) for n=1..32.

Carlos Rivera, Puzzle 232. Primes and Cubic polynomials, The Prime Puzzles & Problems Connection.

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

Example

f(1) = 1^6 - 48*1^5 + 908*1^4 - 8603*1^3 + 42796*1^2 - 105410*1 + 100823 = 30467, a prime number.

Mathematica

Select[Table[n^6-48n^5+908n^4-8603n^3+42796n^2-105410n+100823, {n, 0, 500}], PrimeQ[ # ]&] (* Stefan Steinerberger, Apr 21 2006 *)

Crossrefs

Cf. A005846, A117624.

Sequence in context: A126166 A323754 A251042 * A184788 A043642 A122233

Adjacent sequences: A117088 A117089 A117090 * A117092 A117093 A117094

Keyword

easy,nonn,less

Author

Roger L. Bagula and Parviz Afereidoon (afereidoon(AT)gmail.com), Apr 18 2006

Extensions

More terms from Stefan Steinerberger, Apr 21 2006

Status

approved