Find a prime divisor of 1111 (13 1's)

[mathmadx]

Hello friends,
The problem I am trying to solve sounds simple, but I still haven't been able to find the solution:
Find a prime divisor of 1111111111111 (13 ones), also known as a repunit.
I know the answer(53, 79 and some big prime), but I have no idea how Mathematica calculated those values.
Can anyone help me out? :)

I am afraid I should've posted this question in the number theory forums, sorry for that.

 

[I like Serena]

Hi mathmadx!

As far as I know we're still stuck with trial and error to find prime divisors.
Try each odd number up to the square root and see if it's a divisor.
If you've found one, divide the number and repeat.

 

[spamiam]

An interesting, but probably useless fact from http://en.wikipedia.org/wiki/Repunit" :

It is easy to show that if n is divisible by a, then $R_n$ is divisible by $R_a$:

where $R_i$ is the repunit with i ones. Unfortunately, you're dealing with $R_{13}$ and 13 is prime...