MM127

[LaurV]

Originally Posted by Mini-Geek

Don't worry, it compresses very well. In fact, with the right algorithm, (i.e. "where the bytes of the file as a number are x, calculate MMx") you can store it in a single byte: 01111111.

Hehe, right! Even on a single bit, with "the right" algorithm (like "MMMMM")

[TimSorbet]

Originally Posted by LaurV

Hehe, right! Even on a single bit, with "the right" algorithm (like "MMMMM")

I stopped at MMx because it fit in one byte, and it wasn't SO specific that it was really only intended for this. E.g. any currently-known double Mersenne could be referred to using <= 4 bytes (i.e. an unsigned 32-bit integer, maxing at p=2³²-1~=4.3 billion). That could be reduced to 3 bytes by making it MM (+1 because there is no 0th prime; so rather than make the "convert file to number" concept more complicated, I'll just add 1). In fact, this could refer to future Mersenne doubles <= M310248241 (the 2²⁴th prime) with just 3 bytes! The trouble with this method (using pi(x) in the calculation) is that it can now require some real work just to get p (sure, an efficient sieve can find that in no time, but you still have to correctly implement, or find, an efficient sieve). I think we can spare the extra byte.