One problem is that a black hat could solve a lot of primes in secret, and then use those for a double spend attack.
Specifically,
a) Spend some coins to buy some other cryptocurrency
b) use all their secret primes creating a bunch of new blocks on a branch where they haven't spent their money. Since this is the longest branch now, all the other clients accept they haven't really spent it.
c) buy the other cryptocurrency again on this new branch.
Re:A New Largest-Known Prime Number
by bouncycastle on Saturday December 22, 2018 @11:42AM
(#18741250)
Actually, the problem is that there is no way to control the difficulty. Finding new primes would be harder and harder, but you want the difficulty to adjust up or down to target a block time. Not sure how primecoin approached that problem?
Update: found some clues here, https://www.reddit.com/r/primecoin/comments/1i71ma/strange_b...
Re:A New Largest-Known Prime Number
by man-and-laptop on Saturday December 22, 2018 @07:11AM
(#18740243)
No. The PoW problem should be derived according to the current state of the blockchain. That makes "solving a lot of primes" in secret inapplicable. You read my post far too literally.
The idea is to combine the ideas behind Namecoin with Primecoin.
Re:A New Largest-Known Prime Number
by _trampeltier on Saturday December 22, 2018 @06:10AM
(#18740090)
How would you measure amount of work you want to reward with a coin? In both DNS and torrent examples one can influence a supply of work to be done rather easily
Re:A New Largest-Known Prime Number
by man-and-laptop on Saturday December 22, 2018 @07:12AM
(#18740247)
It's a broad idea to construct a secure PoW, with all that's required to make it secure, but to try and make it applicable to areas like number theory. See PrimeCoin for a successful example.
Also your concerns are unfounded: See Namecoin and Primecoin. I'm thinking these two ideas could be combined.
It makes me think that there should be a list of viable uses of blockchain, and another list of interesting problems that could be moulded into PoWs, and they should be paired up into blockchains.