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A117225
Primes of the form f(n) = 9*n^4 - 444*n^3 + 8059*n^2 - 63714*n + 185371 listed by increasing value of n >= 0.
0
185371, 129281, 86771, 55501, 33347, 18401, 8971, 3581, 971, 97, 131, 461, 691, 641, 347, 61, 251, 1601, 5011, 11597, 22691, 39841, 64811, 99581, 146347, 207521, 285731, 383821, 504851, 1039421, 1287131, 1576321, 1911347, 2296781, 2737411, 3804491, 4441597
OFFSET
1,1
COMMENTS
This polynomial f(n) generates 29 prime numbers consecutively (for n = 0 to n = 28). In n^2 + n + 41, substitute n -> 3*n^2 - 74*n + 430.
REFERENCES
P. Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 2nd ed., 1989, p. 137.
LINKS
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) = 9*1^4 - 444*1^3 + 8059*1^2 - 63714*1 + 185371 = 129281, a prime number.
PROG
(Magma) [a: n in [0..40]| IsPrime(a) where a is 9*n^4-444*n^3+8059*n^2-63714*n +185371]; // Marius A. Burtea, Nov 05 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Roger L. Bagula and Parviz Afereidoon (afereidoon(AT)gmail.com), Apr 21 2006
EXTENSIONS
More terms from Petros Hadjicostas, Nov 04 2019
STATUS
approved