I can't help but clarify this foolishness.

The general Mersenne primes (3,7,31,127,1279,...) between these Mersenne points {1 thru M22}!

Remember all Mersenne primes are general Mersenne primes, but the converse is not true.
If the number of Mersenne primes were finite, then the minimum (k=1), would be excluded from the general Mersenne prime sequence.
Hence making the minimum (k=3), which is absurd.