What are the most famous crypto-currencies which use repeated hashes as proof-of-work?
What are the other proof-of-work methods?
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repeated hashes? most of them use just two repeats.
There are not many other, the vast majority just use two calls to some cryptographic hash function. But a primecoin and cuckoo hash cycle has been suggested. Primecoin arguably searches for some sequence of prime numbers, yet the utility of the result is questionable. On the orher hand the cucoo cycles in hash tables weren't implemented in a practical crypto coin.