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.

(In reply to proof by Jer)

 

A repunit R(n) can only be prime, if n is prime.

 

However this is only a necessary, but not sufficient condition.

The smallest counterexample is R(3) = 111= 3 * 37.

 

Posted by Ady TZIDON on 2011-01-10 17:50:59