Repunits

http://en.wikipedia.org/wiki/Repunit

http://mathworld.wolfram.com/Repunit.html

Repunits: (10^n - 1)/9. Often denoted by R_n.

0, 1, 11, 111, 1111, 11111, 111111, 1111111, 11111111, 111111111, 1111111111, 11111111111, 111111111111, 1111111111111, 11111111111111, 111111111111111, 1111111111111111, 11111111111111111, 111111111111111111, 1111111111111111111, 11111111111111111111

http://oeis.org/A002275

If p(1) = 1, p(2) = 11, p(3) = 111, p(4) = 1111, etc.

where p(n) a 10-base integer represented by a string of n ones.

Most of the repunit numbers are composite.

Indices of prime repunits: numbers n such that 11...111 = (10^n - 1)/9 is prime.

http://oeis.org/A004023

2, 19, 23, 317, 1031, 49081, 86453, 109297, 270343

How do you prove that for p(n) to be prime n has to be a prime number?