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Re:48th Mersenne prime found by ColinWright on Tuesday February 05, 2013 @10:43AM (#5171200)
Not Mersenne Primes, because they have a special structure that can create weaknesses.
Re:48th Mersenne prime found by pbsd on Tuesday February 05, 2013 @12:18PM (#5171817)
While Mersenne primes make breaking discrete logs easier over prime fields, they're pretty OK to use as underlying field on elliptic curve groups (cf. p521).
Re:48th Mersenne prime found by alexkus on Tuesday February 05, 2013 @12:05PM (#5171729)
And such encryption relies on the primes that are used remaining secret.

Using any of the 'well known' primes would be a bad idea as it is easy to go through the 'well known' primes and test to see if they were used as a basis for the encryption.