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)