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Search: id:A117624
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| A117624 |
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List of primes of the form 9*n^6-804*n^5+29836*n^4-588615*n^3+6509950*n^2-38263500*n+93363947 for values of n >= 0. |
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3
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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This polynomial generates 28 consectutive prime numbers for n=0 to n=27.
In n^2+n+41, substitute n -> 3*n^3-134*n^2+1980*n-9663.
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REFERENCES
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P. Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 2nd ed., 1989, p. 137.
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LINKS
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Prime Puzzles, Puzzle 232
Eric Weisstein's World of Mathematics, Prime-generating polynomial""
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EXAMPLE
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9(1)^6-804(1)^5+29836(1)^4-588615(1)^3+6509950(1)^2-38263500(1)+93363947=61050823, a prime number
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MATHEMATICA
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f[n_] := 9n^6-804n^5+29836n^4-588615n^3+6509950n^2-38263500n+93363947; f[Select[Range[0, 100], PrimeQ[f[ # ]] &]] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 16 2006
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CROSSREFS
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Cf. A005846.
Sequence in context: A069318 A015367 A034643 this_sequence A136634 A033625 A128673
Adjacent sequences: A117621 A117622 A117623 this_sequence A117625 A117626 A117627
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KEYWORD
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easy,nonn
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AUTHOR
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Parviz Afereidoon (afereidoon(AT)gmail.com), Apr 08 2006
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EXTENSIONS
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Edited by Don Reble (djr(AT)nk.ca), Apr 14 2006
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