The staying power of this project is very impressive, and the fact that even with the long interval between finds (years) that doesn't seem to detract from dedicating CPU power to the project.
Carbon footprint anyone? ;)
Carbon footprint anyone? ;)
Mₙ = 2ⁿ − 1 gives an easy to generate candidate set and testing primality of a single number isn't that expensive. 57885161th candidate being the 48th hit is getting pretty sparse I guess, but it isn't that crazy. What am I missing? Seems the compute would be rather small compared to much of the "big data" / NN training done every day
You do not check whether that is a prime by trial division (https://en.wikipedia.org/wiki/Trial_division). If you could do a division every nanosecond and had a billion devices, that would still take way, way more time than till the heat death of the universe to do.
We have better tests (https://en.wikipedia.org/wiki/Primality_test#Fast_determinis...), but the best generic one still is Õ((log n)⁶). Here, log(n) is about 58 million, so that log(n)⁶ has over 46 digits.
We can do better, as we don’t need a generic test. for Mersenne numbers, there’s https://en.wikipedia.org/wiki/Lucas–Lehmer_primality_test.
See here for more background:
If you scroll to the very bottom there's some stuff on recent use of probable prime proofs, as well as a fairly detailed explanation of how the whole thing operates.