>presumably go on infinitely long
>presumably go on infinitely long
>I didn't claim there are an infinite number of Mersenne primes.
you actually almost got me :)
The traditional proof that there are an infinite number of primes relies on unique prime factorisation- i.e for any number, n, there is a unique set of primes p1, p2, p3, … etc. where p1 * p2 * p3 * … = n
For instance 88 = 2 * 2 * 2 * 11, 42 = 2 * 3 * 7
It’s worth reading the proof if you haven’t - it’s comprehensible with high school maths.
No such property exists for Mersenne primes, so we can’t trivially extend it. Many proofs of the properties of prime numbers are difficult because they, by definition, actively resist patterns.
I tried some flavors of primes but you'd think the most intuitive one by a magnitude would be listed on the Wiki for proofs.