Oh, right, all Mersenne number is in the form of 2^N -1, but Mersenne prime is Mersenne number plus being prime

And we look for Mersenne primes, AFAIU, mainly because Mersenne numbers are more likely to be prime than other numbers, so it's easier to find big primes that way.

A lot simpler example is 2^4-1=5*3

2^11-1 (prime power) for a less trivial example