Determining Whether the Number $11111$ is Prime. Used Divisibility Tests. I am asked to determine whether the number $11111$ is prime. Upon using the divisibility tests for the numbers 1 to 11, I couldn't find anything that divides it, so I assumed that it is prime. However, it apparently isn't prime. So what is the procedure to determine whether $11111$ is prime?
Thank you for any help.

Not a clean method though but I used Fermat's factorization to find that,
$(105)^2<11111<(106)^2$
Now applying the fact that a perfect square should end only in $0,1,4,5,6,9$, concentrate only on those numbers, the difference of whose square and $11111$ give these digits in the last place. For instance, omit $113,123,133,143$ because the squares of these numbers end with $9$ and would result in $8$ as the last digit and thus this difference will not be a perfect square.
Similarly omit numbers like $112, 122, 132, 142, 152$ (Can you see the reason why?)
On omitting more of such numbers and a little bit of trial, we find that $(156)^2 - 11111 = 13225=(115)^2$
Therefore, $11111 = (156-115)(156+115) = 41.271$
