Looking for a bit of math help

There's an ongoing thread for Lenny Conundrum riddles in... riddles forum. It's been discussed there in detail...

By the way, the answer is "1" if you really wanted to know just that and do the rest by yourself.

I only know the prime number 3..

(3+1)=2*2.

If p is a prime and n is any integer, then

p+1=n^2
or
n^2-1=p
but
n^2-1=(n-1)(n+1)
and if
p=(n+1)(n-1) then p is not prime
so there is no prime in general that satisfy this condition

Special case is n=2 (the only even prime)
p=(2-1)(2+1)=3 (first odd prime)

if n=3, then p=2*4=8 which is not prime

So the only solution is for p=3

3+1=2^2

Rap