Back on the topic of sieve and how it actually relates to the 10M digit test que...
We have sieved almost all the ranges <40T of 991<n<50M, there are a few straggler ranges (pointing my finger at my chest) that have not yet been completed.
I'll release more stats once all these ranges below 40T have been complete. Thus far we have reduced the k/n pair count to ~28700 tests per 1M for the 33-34M level.
To be more specific here is the example of factors found through sieving from 25T to <40T (approx 80% done to 40T) for k=22699
(p=25t) tests within that range at sieve to p=25T
(Current) tests within that range at current sieve point (approx 80% done between 25T to 40T)
Code:
k n=xM p=25T Current Factors
22699 33 1382 1374 8
22699 34 1367 1353 14
22699 35 1416 1402 14
Based upon factor density, a few other considerations and a very rough approximation. We would expect to find 5-10 factors for the 0.5M range we are considering if we sieve to ~70T, (an additional 30T).
Based upon previous post of 2.1% factor chance, 33 hours per P-1 test, and 7 factors found.
It would take us roughly 500 days to find (7) factors through p-1
So if my rough math is correct (which I think it is). it doesn't really make alot sence to P-1 at this point.
Since that exact same machine could sieve 15T (half the range) in the 500 days (30G per day), never mind all the other factors we would find n>20M and those missed factors <20M.
Please don't get me wrong I'm still in 100% favor of the que for n= 10,000,000 digit and the one k approach, I'm just not certain P-1'ing yet is the best thing to do. Start the que regarless it's just more benifital to sieve until say p=75T before we start p-1'ing these numbers. "We eliminate the same number of tests" and "not just the smooth factors".
Point is that even though sieve is not specific to a particular k or n-range. With these low p ranges, the factor density being so high, we eliminate enough in this range just by factor density and probablility to counter act the benifit of the focus of p-1 effort. (hope people/do people follow this???)
I think the major point is we just start the que and keep sieving, perhaps P-1 only the first 5 tests n in the que to fairly high bounds? But no further than we test.