A repunit is a number consisting solely of ones (such as 11
or 11111).

Let us call p(n) a 10-base integer represented by a
string of n ones, e.g. p(1)=1, p(5)=11111 etc.

Most of the repunit numbers are composite.

2, 19,23,317 are
the first four indices of prime repunits.

Prove: For a prime repunit p(n) to be prime, n has to
be prime.