My math teacher gave us problems to work on proofs, but this problem has been driving me crazy. I tried to factor or find patterns in the numbers and all I can come up with is that for $n > 0$, the number $\mod 100$ is $51$ but that does not help. There is definitely an easy way to do this but I can't think of it. Thanks if you can help
Prove that for any nonnegative integer $n$ the number $5^{5^{n+1}} + 5^{5^n} + 1$ is not prime.