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.
This reminded me that I used to leave my computer running Folding@home or similar projects around 2010-2011. Not sure if it ever contributed to anything. If only I had known to run a Bitcoin miner instead!
Back in 2009-2010 I was responsible for deploying 8-16 core servers to customers to run large databases and ERPs. I had the idea of doing some burn in testing to stress the components for around a week for each server. Back then I was aware of bitcoin but also SETI@home. Obviously I chose the second option as I believed it was probable my a better choice for humans kind. It obviously was, but bitcoin mining would have been a better one for me.
I remember some rough calculations suggested I needed to upgrade from agp to pcie to make bitcoin mining worth it financially. I went with boinc instead.
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?)
>(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.
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.
The work in a PoW algorithm has to be otherwise useless in order for it to most effectively deter abuse, or else you'd still be able to get value out of failed attack attempts
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.