1. ## prime number questions

1)if p is bigger than 3 and prime,than prove $p^2+p$is prime.
2) $\forall{n}\in{N},2^{2^n}+1$is prime prove.

2. $p^2+p$ is never prime, because it factorises as $p(p+1)$.

$2^{2^5}+1 = 4294967297 = 641\times 6700417$, so that is not prime either. It is not known whether there is any value of n greater than 4 for which the Fermat number $2^{2^n}+1$ is prime.

3. if p and ${2^p}-1$is prime then prove $2^{p-1}(2^p-{1})$ is a perfect number.