There is (was?) one called riecoin that searched for dense clusters of primes.

I wrote a little about developing a miner for it in 2014: https://da-data.blogspot.com/2014/03/fast-prime-cluster-sear...

There's one called "nexus" that finds sparse clusters of primes of longer length than the ones in riecoin but where there can be a slightly larger inter-prime gap.

(It turns out to be a bad idea to use a mathematically complicated proof of work function, because it means someone like me will come along with some friends who are GPU programming experts and mine your coin better than the developer can.)

I wrote a small paper about developing an optimized technique for mining cuckoo cycle; I believe that technique still forms the basis of how the high performance miners for it work: https://www.cs.cmu.edu/~dga/crypto/cuckoo/analysis.pdf

Monero tried to create a "GPU-resistant" PoW function, so I optimized the CPU miner for it and then we made a GPU version. They've since changed their proof of work function: https://da-data.blogspot.com/2014/08/minting-money-with-mone...

(The funny part of that monero one, of course is that the publicly released miner at the time had been artificially slowed down by the bitmonero devs so they could pre-mine it)

> Does anyone know other innovative PoW chains?

Wikipedia gives some ideas:

https://en.wikipedia.org/w/index.php?title=Proof_of_work&old...

https://en.wikipedia.org/w/index.php?title=Proof_of_work&old...

For example

* Cuckoo Cycle: https://docs.grin.mw/wiki/miscellaneous/cuckoo-cycle/

* The paper "Ofelimos: Combinatorial Optimization via Proof-of-Useful-Work A Provably Secure Blockchain Protocol": https://crypto.iacr.org/2022/papers/538804_1_En_12_Chapter_O...

Quote from Wikipedia concerning Ofelimos: "At the IACR conference Crypto 2022 researchers presented a paper describing Ofelimos, a blockchain protocol with a consensus mechanism based on "proof of useful work" (PoUW). Rather than miners consuming energy in solving complex, but essentially useless, puzzles to validate transactions, Ofelimos achieves consensus while simultaneously providing a decentralized optimization problem solver. [...] The paper gives an example that implements a variant of WalkSAT, a local search algorithm to solve Boolean problems.|"

Monero's RandomX is an interesting PoW scheme one designed to be optimized for CPUs. Here is an interesting read about its design https://github.com/tevador/RandomX/blob/master/doc/design.md

Chia uses a very memory-hard PoW system and is usually mined on SSDs.

I've seen a lot of "useful PoW" cryptocurrencies, but they tend to not pan out. For example Gridcoin is just a Proof-of-Stake cryptocurrency with a program that hands out GRC to BOINC contributors.

Though if you click on "Mkt Cap" and "All" time, you see that Primecoin had a market cap high in 2018-03-05 with USD 83.029M and on 2021-11-18 with 64.8764M.