Sophie Germain primes are a special class of prime numbers that have a unique property. A prime number p is called a Sophie Germain prime if 2p + 1 is also a prime number. For example, if we take the prime number 5, we find that 2 \times 5 + 1 = 11 , which is also prime. These primes are named after the French mathematician Sophie Germain, who made significant contributions to number theory in the early 19th century. Sophie Germain primes are of interest in various fields, including cryptography, due to their mathematical properties and relationships with other prime numbers.