A Germain prime is a special type of prime number that is one less than a power of two. Specifically, if p is a Germain prime, then 2p + 1 must also be a prime number. For example, if p = 2 , then 2 \times 2 + 1 = 5 , which is prime. These primes are named after the French mathematician Pierre de Fermat, who studied prime numbers extensively. Germain primes are of interest in number theory and have applications in cryptography, particularly in algorithms that rely on prime numbers for secure communication.