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 re(2): proof by Jer)

Nothing wrong with your proof, I agree with all your statements, as the Bard said..."to the selfsame tune and words".

 

Whatever I added was a remark , to distinguishb between necessary and sufficent-  with no claim re anything you wrote.

To sum uo:  conrapositives are of equal weight.

 

Posted by Ady TZIDON on 2011-01-11 12:43:46