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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.



Don't forget:

Primemarkcoin

Perceptiongapcoin

Liecoin

epiplexiscoin

and of course, the every useful pyramidcoin and scamcoin.




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