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).
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.
