Primecoin is new, is that all?! What innovation??! Which of Bitcoin addressed flaws it improves or solves??!
The part where all of the immense amounts of hashing power results in nothing more than a verification of the latest block.
then where the resulted prime list is stored now for the use of number theorists?!
In the blockchain. You can query it with the getblock command. There's already a few 3rd party programs that analyze the chain.
(putting aside the fact that there are a lot of more clever and faster ways-sieves of finding primes inside math community already, if you need some I can refer you to)
Have you read anything in this thread? It's not about finding primes, it's about prime chains. But if one does know a faster method, then it would be profitable to write a miner that uses it. I don't see how that's a criticism of primecoin at all. The method of finding blocks to mine isn't set in stone.
Besides using a new (interesting I confess) way of encryption, the only benefit I see from this new (come and leave) altcoin is for dearest miners and darling speculators to benefit the pyramid.. yes the price will rock for a while, because it is new and looks attractive (very american, isn't it?!) so if you did buy a lot when the prize was 10 cents or mined when the diffculty was <1, you win some money..and then it will go to the list of alt-coin stories.
The same thing happened with Bitcoin.