https://en.wikipedia.org/wiki/List_of_Mersenne_primes_and_pe...
If this happened the way you remember, it's really unfortunate, but it wouldn't have stopped the prime in question from being discovered, because GIMPS always at least eventually gives out numbers to multiple people to check, and doesn't mark Mersenne numbers as checked until a computer actively reports that they were checked.
However, your name could have ended up on that Wikipedia list as a discoverer. :-)
But it doesn't, and unfortunately even worse, it wasn't ASIC-resistant, which had second-order effects that Intel could had actually taken advantage of if they werent sleeping from being too comfortable.
I found this but curious what else exists! https://en.wikipedia.org/wiki/Primecoin
the difficulty of the work must be adjustable,
the difficulty/reward ratio must scale to the polynomial of users/work-rate to avoid sybil/"51% (31%)" attacks, and dissuade volatility during transitions
must be easily verifiable,
Primecoin uses Cunningham Chain primes - basically sequences of primes where 2x+1 is prime.
They are marginally useful with other applications on the horizon.
I could see adjusting the arbitrary rule-set - similar to the varying rulesets of cellular automata, like Conways - to further Number Theory/Game Theory/Swarm Economics at a general interdisciplinary level to be the most potentially rewarding, covering a larger swath of unknown unknowns.
>(for instance what happens when you prove a prior established complexity wrong?)
No stakes, no steaks!
But it does seem interesting - counterintuitive really, but a "Busy Beaver" / proof of work verifying mechanism enumerating inputs/instructions/outputs randomly (or whatever the nodes think they know best at ) while rewarding (only? why not top 3?) the shortest, most efficient block...could be tweaked to crunch ETH contracts like gas, brute-force fuzz-test legacy unsafe sourcecode...literally a foundation for further distributed computation.
There are languages like it - Dennis and his Bubblegum - that have generative, selective, and compressive patterns interned already.
10 years!
Gapcoin (finding large gaps between successive primes)
Riecoin (finding maximally dense prime clusters of size 6)
Nexus (finding almost-dense clusters with a maximum spacing between successive primes)
As an aside, picking a mathematically interesting and intricate proof of work function is probably a bad idea, because someone like me will come along and optimize the miner and mine privately at a large profit margin, as I did with two of these coins.