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Search: id:A087277
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| A087277 |
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Numbers n such that the three second-degree cyclotomic polynomials x^2 + 1, x^2 - x + 1 and x^2 + x + 1 are simultaneously prime. |
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1
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| 2, 6, 90, 960, 1974, 2430, 2730, 2736, 6006, 6096, 6306, 7014, 11934, 14190, 18276, 18486, 21204, 24906, 24984, 25200, 27210, 35700, 38556, 39306, 40860, 44694, 45654, 47124, 49524, 51246, 53220, 56700, 58176, 63330, 63960, 72996, 76650
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OFFSET
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1,1
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COMMENT
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It appears that all these n, except n=2, are multiples of 6. By Schinzel's hypothesis, there are an infinite number of n that yield simultaneous primes. Note that the two first-degree cyclotomic polynomials, x-1 and x+1, yield the twin primes for the numbers in A014574.
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REFERENCES
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P. Ribinboim, The New Book of Prime Number Records, Springer, 1996, p. 391
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
Eric Weisstein's World of Mathematics, Schinzel's Hypothesis
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EXAMPLE
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6 is a member of this sequence because 31, 37 and 43 are primes.
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MATHEMATICA
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x=0; Table[x=x+2; While[ !(PrimeQ[1+x^2]&&PrimeQ[1+x+x^2]&&PrimeQ[1-x+x^2]), x=x+2]; x, {50}]
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CROSSREFS
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Cf. A014574.
Sequence in context: A109892 A055702 A128265 this_sequence A007188 A129364 A092287
Adjacent sequences: A087274 A087275 A087276 this_sequence A087278 A087279 A087280
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Aug 27 2003
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