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Re:New Mersenne Prime discovered (probably) by Jerrrrrrry on Saturday October 19, 2024 @12:13AM (#41885586)
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.

Re:New Mersenne Prime discovered (probably) by aphantastic on Saturday October 19, 2024 @12:24AM (#41885622)
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?)
Re:New Mersenne Prime discovered (probably) by Jerrrrrrry on Saturday October 19, 2024 @01:01AM (#41885752)

  >(for instance what happens when you prove a prior established complexity wrong?)

what do you mean? you run their wallets, pun intended!

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.

https://esolangs.org/wiki/Bubblegum

Re:New Mersenne Prime discovered (probably) by tromp on Saturday October 19, 2024 @04:25AM (#41886478)
You forgot one important property: it must commit to the new block(header).