Math is hard
If the number of Mersenne primes is finite, there is a largest Mersenne prime, call this 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.
Happy computing, or better: Do some hard thinking.