Re: Math is hard
"Mlargest. This is a prime number from which the number (2^Mlargest)-1 can be derived. Because this can not be a prime, it should be the product of two or more primes. At least one of its factors is expected to be larger than Mlargest."
Congratulations, you have proved that large numbers exist.
Problems with your proof:
1) All factors could be smaller than Mlargest.
2) The factors need not be Mersenne primes.
There's a reason that some problems are hard. It's not that mathematicians are bumbling idiots.