Hunting Million-Digit Primes from My Loft
primecrunch.com
primecrunch.com
SETI@home is gone but Folding@home is still very much a thing. There are currently 133 active projects: https://apps.foldingathome.org/psummary
The mathematical tools which people develop along the way to finding them can be useful for other number theory problems.
It is also a concise statement that is trivial to verify.
(by "trivial" meaning much much easier to verify than to discover in the first place)