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Smallest number x such that the first n cyclotomic polynomials evaluated at x are primes.
1

%I #7 Oct 19 2017 03:14:01

%S 3,4,6,6,1068630,6770610,2981997480,339126523890,120351747887280,

%T 13533264289711320

%N Smallest number x such that the first n cyclotomic polynomials evaluated at x are primes.

%C Let Phi_k be the k-th cyclotomic polynomial. a(n) is the least integer x such that for each k from 1 to n, Phi_k(x) is prime.

%e a(6)=x=6770610 because Phi_1(x)=x-1, Phi_2(x)=x+1, Phi_3(x)=x^2+x+1, Phi_4(x)=x^2+1, Phi_5(x)=x^4+x^3+x^2+x+1 and Phi_6(x)=x^2-x+1 are all prime.

%Y Cf. A014574, A070020, A070025, A070043.

%K nonn

%O 1,1

%A _Don Reble_, May 15 2002 and _Phil Carmody_, Aug 09 2002