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

1. Oct 30, 2011

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.

2. Oct 30, 2011

### I like Serena

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.

3. Oct 30, 2011

### spamiam

An interesting, but probably useless fact from http://en.wikipedia.org/wiki/Repunit" [Broken]:
where $R_i$ is the repunit with i ones. Unfortunately, you're dealing with $R_{13}$ and 13 is prime...

Last edited by a moderator: May 5, 2017