A070737 Smallest number x such that the first n cyclotomic polynomials evaluated at x are primes.

3, 4, 6, 6, 1068630, 6770610, 2981997480, 339126523890, 120351747887280, 13533264289711320

Offset: 1

Author

Don Reble, May 15 2002 and Phil Carmody, Aug 09 2002

Keywords

• nonn

Comments

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.

Examples

			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.
		

Crossrefs

Cf. A014574, A070020, A070025, A070043.