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A safe prime is a prime number of the form 2p + 1, where p is also a prime.  It can be noted that the prime p is a Sophie Germain prime.  Some small safe primes include:

5, 7, 11, 23, 47, 59, 83, 107, 167, 179, 227, 263, 347, 359, 383, 467, 479 ...

With the exception of 7, a safe prime q is of the form 6k−1, in other words, these safe primes are one less than a multiple of six.  Also, with the exception of 5, a safe prime is of the form 4k−1, in other words, these safe primes are one less than a multiple of four.  Also, with the exception of 7, there are no safe primes that are also Mersenne primes

Safe primes found its usefulness and importance in cryptography and information security, especially in the present era when many vital information are transmitted through the internet.


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