I have a very strong academic mathematics background. 'scientific value' is a subjective statement. Most mathematicians would regard anything new or original as advancing mathematics. Do you think patterns in integers have scientific value? Depends on the pattern to an extent and if there are any clear consequences but you'll get varied answers to that question. Some mathematicians and especially scientists such as physicists are snobbish and only regard maths that has a 'real world' application as being useful. It's not clear to me whether this project is finding new prime chain sequences within the known prime numbers or actually trying to determine new, unknown prime numbers using the prime chains as a proof of work. Either way, it has value since it will add new data which will either disprove conjectures or strengthen the likelihood of them being true... plus the analysis of the discovered data could in theory lead to new conjectures (note I know next to nothing about these chains and how much data of them is out there, I'm just writing this reply of the top of my head).

You can also look at this another way. This project could provide a financial incentive for individuals to develop more optimised GPU prime finding algorithms, the theory of which could lead to a greater understanding of prime number distribution e.g. a new sieve or similar construct.

You can also look at this another way. This project could provide a financial incentive for individuals to develop more optimised GPU prime finding algorithms, the theory of which could lead to a greater understanding of prime number distribution e.g. a new sieve or similar construct.

**Sunny**, can you please clarify whether this project is finding new prime chain sequences within the known prime numbers or actually trying to determine new, unknown prime numbers using the prime chains as a proof of work.Of course these primes are all 'new'. Finding 'new' primes is not the point, and primes are super-abundant there is no database can store them, it's always trivial to find one not stored in any database.

The point of GIMP is to find the largest known (Mersenne) prime, while the point of primecoin is to find longest chain of reasonable size limit (256 bits to 2000 bits as currently designed). Which one of the two projects is more useful is highly debatable actually. Mersenne has a very long history of study, its infinite existence is not known and they are scarce (only about 50 of them known). While for prime chains, as pointed out by my design paper, these prime chains are connected to the distribution of primes, their infinite existence and distribution is among the top wonders of arithmetic, you know how much mathematician value twin prime conjecture right? At right now I think some mathematicians consider the distribution of these longer chains hopelessly untouchable, and maybe will stay another millenium

2^256 is WAY bigger than 2048. 2048 is 2^11.