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 A117624 Primes of the form f(n) = 9*n^6 - 804*n^5 + 29836*n^4 - 588615*n^3 + 6509950*n^2 - 38263500*n + 93363947 for values of n >= 0. 3
 93363947, 61050823, 38620051, 23498297, 13649371, 7493947, 3835763, 1794301, 743947, 259631, 68947, 10753, 251, 547, 691, 197, 43, 151, 3347, 25801, 113947, 367883, 971251, 2227597, 4603211, 8776447, 15693523, 26630801, 102768947, 218611051, 1738931741 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This polynomial f(n) generates 28 consecutive prime numbers for n = 0 to n = 27. In n^2 + n + 41, substitute n -> 3*n^3 - 134*n^2 + 1980*n - 9663. REFERENCES P. Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 2nd ed., 1989, p. 137. LINKS Carlos Rivera, Puzzle 232, The Prime Puzzles & Problems Connection. Eric Weisstein's World of Mathematics, Prime-generating polynomial. EXAMPLE f(1) = 9(1)^6 - 804(1)^5 + 29836(1)^4 - 588615(1)^3 + 6509950(1)^2 - 38263500(1) + 93363947 = 61050823, a prime number. MATHEMATICA f[n_] := 9n^6-804n^5+29836n^4-588615n^3+6509950n^2-38263500n+93363947; f[Select[Range[0, 100], PrimeQ[f[ # ]] &]] (* Stefan Steinerberger, Apr 16 2006 *) CROSSREFS Cf. A005846. Sequence in context: A186051 A205665 A205465 * A147527 A293244 A136634 Adjacent sequences:  A117621 A117622 A117623 * A117625 A117626 A117627 KEYWORD easy,nonn AUTHOR Parviz Afereidoon (afereidoon(AT)gmail.com), Apr 08 2006 EXTENSIONS Edited by Don Reble, Apr 14 2006 More terms from Petros Hadjicostas, Nov 04 2019 STATUS approved

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Last modified June 29 05:16 EDT 2022. Contains 354910 sequences. (Running on oeis4.)