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Is there a good POW mechanism that would test primes? I found this but curious what else exists! https://en.wikipedia.org/wiki/Primecoin https://en.wikipedia.o

Is there a good POW mechanism that would test primes? I found this but curious what else exists! https://en.wikipedia.org/wiki/Primecoin https://en.wikipedia.org/wiki/Primecoin

Jerrrrrrry 2y ago
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.
- aphantastic 2y ago
  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?)
  - Jerrrrrrry 2y ago
    >(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 https://esolangs.org/wiki/Bubblegum
- tromp 2y ago
  You forgot one important property: it must commit to the new block(header).
tromp 2y ago
There's also https://gapcoin.org/ https://gapcoin.org/ for searching prime number gaps (mine the gap).
- Jerrrrrrry 2y ago
  I knew I forgot something, thank you! 10 years!
  - tromp 2y ago
    There's also https://riecoin.xyz/ https://riecoin.xyz/ searching prime constellations.
dgacmu 2y ago
Primecoin (Cunningham chains) 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.
- einpoklum 2y ago
  Don't forget: Primemarkcoin Perceptiongapcoin Liecoin epiplexiscoin and of course, the every useful pyramidcoin and scamcoin.

Is there a good POW mechanism that would test primes? I found this but curious what else exists! https://en.wikipedia.org/wiki/Primecoin https://en.wikipedia.org/wiki/Primecoin

Jerrrrrrry 2y ago

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.

aphantastic 2y ago
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?)
- Jerrrrrrry 2y ago
  >(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 https://esolangs.org/wiki/Bubblegum
tromp 2y ago
You forgot one important property: it must commit to the new block(header).

tromp 2y ago

There's also https://gapcoin.org/ https://gapcoin.org/ for searching prime number gaps (mine the gap).

Jerrrrrrry 2y ago
I knew I forgot something, thank you! 10 years!
- tromp 2y ago
  There's also https://riecoin.xyz/ https://riecoin.xyz/ searching prime constellations.

dgacmu 2y ago

Primecoin (Cunningham chains) 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.

einpoklum 2y ago
Don't forget: Primemarkcoin Perceptiongapcoin Liecoin epiplexiscoin and of course, the every useful pyramidcoin and scamcoin.