The PPS is far, far above 4 million; Otherwise I'd be getting far more blocks with my 15k PPS.

what is the diff = function (?)

20XPM/block at the beginning. But I have no idea why 15.xx now . It's depend on total PPS, isn't it?

assuming a 4M pps network and that probability is proportional to pps, for each thousand of pps you should get four blocks per day.

How do you increase the number of connections? any nodes to be added? I have only 8 connections at the moment.
thanks

I'm not sure this is the case, or at least it is not as simple.  With hashcash proof-of-work it is impossible to look for lower difficulty shares without also looking for higher difficulty shares.  In Primecoin, on the other hand, as I understand it, one could look for chains of length 7 and find them with much greater frequency than they would find chains of length 7 while looking for chains of length 8 (i.e. pool miners would maximize their share submission by hurting the pool; the tragedy of the commons ensues).

I assume that when the mining algorithm executes it first executes the Sieve of Eratosthenes to build a list of possible primes.  If one finds that there is a list of 7 numbers that passed the sieve and form a chain then they could be checked to see if they form a valid share, even if the sieve eliminated the next value, proving that a block of difficulty 8 or higher is impossible from that start (I am assuming a share difficulty of 7 and a network difficulty of 8 or more).  A miner optimized for finding valid blocks as fast as possible would save computational time by ignoring the chain of length 7 when the difficulty is 8 or higher, while a miner optimized for finding valid shares would check every chain of primes that passes the sieve that is at least (share length) long.

This could be circumvented by requiring the numbers after the share's chain up to the integral network difficulty to all pass a sieve, but I believe that that would break the requirement that shares be fast to verify by the pool host.  Additionally, it would set stringent requirements on how the numbers would have to be sieved which would limit improvements to be made in that area (which seems to be where most of the improvements are being made).

You've made a really innovative coin, Sunny, and I trust you to come up with an innovative solution to this, but it isn't as simple as it may appear at first glance.

Is anyone who's tech savvy enough making a pool? You can make a shit ton of coins since everyone would hop right on.

How much primecoins will be generated at all?

I didn't say there is no logic in much of you've said, on the contrary, your explanation why other coins fail is interesting. I only think you underestimate the inertia of Bitcoin fundamentals, it *may* fork in a few decades if SHA256 is undermined, and it may switch to some new hash function but everything else will stay the same.

Also, you are underestimating the new fundamental advantage of Primecoin: it will be very hard to implement it in GPU to be faster than CPU, unlike other coins. The advantage to mine with only CPU, gives many people a chance to mine, taken away from them by specialized GPU mining monsters.

I think you just proved my point here.