While I was exploring multiplication tables I stumbled on something cool.
Take any power of 2 on the multiplication chart.
Now look at the number in the bottom left adjacent box.
The difference of these two numbers will always be a Mersenne number.
Go ahead. Starting on the 2's column of a multiplication table, look in the bottom left of each power of 2 and get the difference.

2-2 = 0
4-3= 1
8-5 = 3
16-9=7
32-17=15

etc.

While the online journal of integer sequences lists a lot of forumlas, I just wrote what came to mind (I'm sure its already known):
((2**i)-(((2**i)/2)+1))

The interesting thing about this is it generates not only the Mersenne numbers, but if you run i *backwards* it generates *additional* numbers.
So its a superset of mersenne numbers.

at i = 0 we get -0.5
i=-1 -> -0.75
i=-2 -> -0.875
i=-3 -> -0.9375
i=-4 -> -0.96875

And while this sequence is *not* mersenne numbers, mersenne numbers *are* in this set.

Just a curious discovery is all.

I was looking for the largest known mersenne prime and tried doing this. I guess these are language limitations and don’t know what type of computers can give instant answers for such mathematical calculations. Is this complex than bitcoin hash? May be