# Generator of P but not Q

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 $$p$$.

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