Germain primes are a special type of prime number. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A Germain prime is defined as a prime number p such that 2p + 1 is also a prime number. For example, if p = 5 , then 2 \times 5 + 1 = 11 , which is also prime. These primes are named after the French mathematician Pierre Germain. Germain primes are relatively rare compared to other types of primes. They are of interest in number theory and have applications in cryptography, where prime numbers play a crucial role in securing data.