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Safe and Sophie Germain primes

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Safe primes and Sophie Germain primes are specific types of prime numbers with particular mathematical properties. ### Sophie Germain Primes A prime number \( p \) is called a *Sophie Germain prime* if \( 2p + 1 \) is also a prime number. In other words, for a prime number \( p \), if \( q = 2p + 1 \) is also prime, then \( p \) is classified as a Sophie Germain prime.

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