The story
From safe (adjective) + prime (noun). These primes are called “safe” because they are safe to use in cryptography due to the fact that one less than the prime has the largest possible prime factor.
Etymology from Wiktionary, CC BY-SA 4.0.
safe prime
Today it means: A prime number of the form 2p+1, where p is also a prime (the latter is called a Sophie Germain prime). Full definition →