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A233512
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The first n cyclotomic polynomials are simultaneously prime for these arguments.
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1
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OFFSET
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1,1
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COMMENTS
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The first six cyclotomic polynomials are x - 1, x + 1, x^2 + x + 1, x^2 + 1, x^4 + x^3 + x^2 + x + 1, and x^2 - x + 1.
By Schinzel's hypothesis H, this sequence is defined for all n.
a(7) > 2*10^9.
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REFERENCES
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LINKS
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EXAMPLE
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At x = 3, x-1 = 2, which is prime. At x = 4, x-1 = 3 and x+1 = 5, which are both prime. At x = 6, x-1 = 5, x+1 = 7, and x^2+x+1 = 43, which are all prime.
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MATHEMATICA
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t = {}; n = 0; len = 0; While[len < 6, n++; found = True; i = 1; While[found && i <= len + 1, found = PrimeQ[Cyclotomic[i, n]]; i++]; If[found && i > len + 1, AppendTo[t, n]; len++]]; t
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CROSSREFS
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Cf. A014574 (first degree solutions: average of twin primes).
Cf. A087277 (similar, but with second-degree cyclotomic polynomials).
Cf. A231612 (similar, but with fourth-degree cyclotomic polynomials).
Cf. A231613 (similar, but with sixth-degree cyclotomic polynomials).
Cf. A231614 (similar, but with eighth-degree cyclotomic polynomials).
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KEYWORD
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nonn,hard,more
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AUTHOR
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STATUS
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approved
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