New Mersenne Prime discovered (probably)

I can swear something like 20+ years ago I found a new one too, but I didn’t realize the importance of it. I had just downloaded GIMPS and I was just messing around with it, and when I saw the message I thought “ok, cool!” and proceeded to turn it off.

If it was literally around "20+ years ago", like 2004 or slightly before, it might have been M40 or M41.

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. :-)

Interesting that all the primes since 2001 have been discovered by Intel processors (at least those where the processor was recorded). How’s that for marketing?

If bitcoin used a facet of primality in its Proof-of-Work, that would nearly needlessly gloating.

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.

Is there a good POW mechanism that would test primes?

I found this but curious what else exists! https://en.wikipedia.org/wiki/Primecoin

Thats it (afaik), and it could be for the usual, dismissive reasons, but its easy to hand-waive the "make primality a part of the work" part but it also comes down to the properties of the work that require it to be useful:

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.

My favorite “Practical POW” remains komoglorav complexity computation. The reward would likely scale with the runtime needed to verify a complexity, but there’s plenty of room for subtleties in the implementation. (for instance what happens when you prove a prior established complexity wrong?)