Prime density

[Lagardo]

Years back when I singed up for SOB, there were a couple people trying to get a bit of a handle on the expected probabilities for primes found. The exact numbers varied a little up or down depending on who's assumptions you bought, but the bottomline that I recall went something like this:

SOB has a realistic chance of finding six primes, maybe seven. If and when they hit eight, people just looking to find big primes should go to GIMPS or something, as the actual probability of a ninth or even tenth were so close to zero (with the given algorithm) as to be negligible.

I'm kinda curious what the current thinking on this is -- not from the people who just have an opinion, but from those who have some math to back it up (I don't mind the opinions, but it's the math I'm interested in). What is the current expectation value for the time to the next prime/s, given some reasonable assumptions about the development of the total number crunching power (number of ppl, avg. flops per computer etc).

[vjs]

I'm just going to give an opinion here and say check other posts for the math.

Alot has changed since those many years back. First there wasn't very many people so back then and checking n>10M seemed like a monumental task. Second I don't know of any reason why gimps numbers are more likely to yeild primes than SoB numbers with equal efforts put into factoring and sieving.

Now as to the exact number of primes this project should find... When making quotes of only finding 8 primes before we should stop. That was based on the opinions that we wouldn't find our 9th prime before 20M if I recall. Considering we have found 8 already before n=10M and the possibility exists that we missed one prime... I don't see us stopping anytime soon. One also has to consider that we have found a majority of the light k's already so the possibility of another 4 primes or more before 20M is quite high.

Third several people including myself are already sieving for n>20M so the project will continue for several years to come.

If you want actual math on any particular aspect please ask a specific someone will chime in, I'm pretty sure people enjoy discussions like these just remember it's all probability.