Sophie Germain prime

A Sophie Germain prime is a prime p for which 2p+1 is also prime. The larger prime 2p+1 is then called a safe prime. They are named after Sophie Germain.

Key features

• The first few are 2, 3, 5, 11, 23, 29, 41, 53, 83, 89.
• Used in cryptography (e.g. safe primes in Diffie–Hellman).

Examples:

2, 3, 5, 11, 23, 29, 41, 53, 83, 89

Further reading

• Sophie Germain prime on Wikipedia
• Sophie Germain prime on OEIS