A117225 - OEIS

%I #32 Feb 16 2025 08:33:00

%S 185371,129281,86771,55501,33347,18401,8971,3581,971,97,131,461,691,

%T 641,347,61,251,1601,5011,11597,22691,39841,64811,99581,146347,207521,

%U 285731,383821,504851,1039421,1287131,1576321,1911347,2296781,2737411,3804491,4441597

%N 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.

%C 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.

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

%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_232.htm">Puzzle 232. Primes and Cubic polynomials</a>, The Prime Puzzles & Problems Connection.

%H Eric Weisstein's World of Mathematics <a href="https://mathworld.wolfram.com/Prime-GeneratingPolynomial.html">Prime-generating polynomial</a>.

%e f(1) = 9*1^4 - 444*1^3 + 8059*1^2 - 63714*1 + 185371 = 129281, a prime number.

%o (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

%Y Cf. A005846, A117624, A117090, A117091.

%K easy,nonn,changed

%O 1,1

%A _Roger L. Bagula_ and Parviz Afereidoon (afereidoon(AT)gmail.com), Apr 21 2006

%E More terms from _Petros Hadjicostas_, Nov 04 2019