this is all very cool, but i fail to see the need for prime numbers this large, other than so you can brag about the record to your fellow nerds of course.
(These aren't particularly large for prime numbers. They're big for prime number chains.) Some mathematicians may find this data useful. That's already infinitely more valuable than the results of bitcoin's sha256 / litecoin's scrypt random proof-of-work statements outside of the context of the currency.
good point, however i disagree that they are "infinitely more valuable". one has scientific value(which in my mind is debatable) and one has security(proven until its broken.) seems like an apples and oranges argument to me.
Primecoin's has both.
I find it a bit disappointing that for all of the extreme amounts of computational power that goes into Bitcoin's blockchain, all we get is a verification of the latest block. There's no interesting analysis possible of the proof-of-work statements. Primecoin at least doubles as an enormously huge chain of mildly interesting computations.
quick, lets make UFO coin. every signal decrypted and processed is a block. first person who decrypts it a processes is rewarded the block. now we have another scientific coin. see where i'm going with this? you know, at first i was being facetious but you just might have sold me. maybe scientific computations offered by prime and any future coins like it could offer a pseudo-backing for the currency, much in the way that physical gold and silver once backed physical paper money