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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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A254772 A254779 A254725 * A032748 A180099 A092013
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

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Last modified May 25 12:25 EDT 2024. Contains 372788 sequences. (Running on oeis4.)