What’s prime grid
So a hobby of number fans and mathematicians alike is looking for big prime numbers. Because if you find one, you’ll have a small dose of fame (and sometimes prize money). Of course, the prime numbers we know of are so large that you can’t feasibly check them all by hand anymore, so you have to get computers to run them.
There are two competing projects to find big prime numbers: GIMPS and PrimeGrid. GIMPS (Great Internet Mersenne Prime Search) is dedicated to finding bigger and bigger Mersenne Primes (2^n -1), because Mersenne primes are really easy to check—their sieve is really simple for binary computers.
PrimeGrid runs a bunch of other sieves looking for different kinds of prime numbers, like 321 primes (3*2^n ±1), Proth Primes (k*2^n +1), Cullen/Woodall Primes (n*2^n ±1), Generalized Fermat Primes (b^2^n +1), and more. These aren’t necessarily going to be the biggest, but they are mathematically interesting for other reasons. For example, there’s an attempt to solve the Sierpiński problem (is 78557 the smallest k for which no Proth Primes exist?), called “Seventeen or Bust” (because there were 17 candidates when they started), which had found the 7th largest prime number (since dropped down to 11th place) by eliminating one of those candidates (there are now only 5 candidates). Of course, you can try to find the biggest prime number with their “Do you feel lucky?” project (“a real long shot. It borders on stupidity”).
Both of these you can run in the background on your computer, donating your excess computing power to advancing mathematics. GIMPS is its own standalone program. PrimeGrid runs thru BOINC (Berkeley Open Infrastructure for Network Computing), which you may know from Einstein@Home, Rosetta@home, or World Community Grid.
