A safe prime is a special type of prime number that can be expressed in the form 2p + 1, where p is also a prime number. This means that safe primes are always one more than twice another prime. For example, if p = 3, then 2 \times 3 + 1 = 7, which is a safe prime. Safe primes are important in cryptography, particularly in algorithms like the Diffie-Hellman key exchange and the RSA algorithm. Their unique properties help ensure secure communication by making it difficult for attackers to factor large numbers, which is a common method used in breaking encryption.