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# 25475...67041 (6716-digits)

This number is a prime.

The generalized repunit (675065^{1153} - 1)/675064 is prime.

A proof is possible because of the remarkable circumstance that, for
*b* = 5*37*41*89 and *p* = 2^{7}*3^{2}+1,
both Phi(*p*,*b*) and Phi(*p*-1, *b*) are prime,
where Phi(*n*, *x*) is the *n*^{th} cyclotomic polynomial
in *x*. [Broadhurst]

Printed from the PrimePages <t5k.org> © G. L. Honaker and Chris K. Caldwell