I think it useful to discuss what are the general capacities of "code crackers" to find prime factors in "large numbers." Well, about 20 years ago it was generally thought that if two 100 digit primes were multiplied together it was as a practical matter impossible to factor this 200 digit number. This fact was used in constructing secret codes.
Well, today on the internet I found this: This function creates keys using the method described in the Procedure section. It first generates two 100-digit prime numbers p and q by initializing them both to 10100 and incrementing them by 1 and -1, respectively. Each time they are incremented, they are tested for primality. In this way, p and q were found to be:....
The writer then is suggesting that as a general rule such 200 digit numbers can not be factored as a practical matter. http://ashvin.flatirons.org/projects...e/results.html
You have to understand that a Mersenne prime is a special case where mathematicians and programmers use special criterion to work with.