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Search: id:A117090
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| A117090 |
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Primes of the form 9n^4-204n^3+1777n^2-7038n+10729. |
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+0
2
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| 10729, 5273, 2273, 829, 257, 89, 73, 173, 569, 1657, 4049, 8573, 16273, 28409, 46457, 72109, 107273, 154073, 214849, 292157, 507673, 825389, 1883773, 2260529, 4357673, 5834657, 8717273, 19496657, 26342573, 31815257, 67625969, 104356457
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OFFSET
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1,1
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COMMENT
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This polynomial generates 20 prime numbers consecutively (for n=0 to n=27). In n^2+n+17, substitute n -> 3n^2-34n+103. in Euler equation (n^2+n+q for q=17)polynomial generates 16 prime numbers consecutively (n=0 to n=15).
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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 puzzle
Eric Weisstein
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EXAMPLE
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a(1)=9(1)^4-204(1)^3+1777(1)^2-7038(1)+10729=5273, a prime number
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MATHEMATICA
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Select[Table[9n^4 - 204n^3 + 1777n^2-7038n+10729, {n, 0, 500}], PrimeQ[ # ]&] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 21 2006
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CROSSREFS
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Cf. A005846, A.117624.
Sequence in context: A006006 A023941 A065320 this_sequence A023084 A034231 A010089
Adjacent sequences: A117087 A117088 A117089 this_sequence A117091 A117092 A117093
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KEYWORD
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easy,nonn,less
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com) and Parviz Afereidoon (afereidoon(AT)gmail.com), Apr 18 2006
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EXTENSIONS
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More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 21 2006
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