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A prime $q$ such that $2q+1$ is also a prime is a Sophie Germain prime. Cramer's conjecture tells gap between consecutive primes is bound by $O(\log^2p)$. Is there a similar conjecture for Sophie ...

This is a follow-up question, which is related to the answer of this quesiton: Is there a connection of prime numbers and extreme value theory? I will duplicate the answer here, so this question is ...