# Generator of P but not Q

**Number Theory**Level 5

Find the sum of all primes \(p<100\) such that \(q=2p+1\) is a prime, and \(2\) is a generator modulo \(p\), but not modulo \(q\).

**Details and assumptions**

A residue \(a\) is called a **generator modulo prime \(p\)** if every non-zero residue modulo \(p\) equals some power of \(a\) modulo \(p\).