Remaining test density

[philmoore]

I am curious - about how many k/n pairs remain in the range 10 million to 20 million, now that only 8 k remain? At the beginning of this project, the number of tests in a given range exceeded the number of GIMPS candidates, but I suspect that has changed now. If GIMPS was able to eliminate 60% of possible candidates by factoring, they should have had to do around 240,000 to 250,000 primality tests in the range 10M to 20M. At this point, I would not expect sieving and factoring to eliminate more than 1-3% of the remaining SoB tests, so we should be able to get a good idea of the relative density of candidates now.

[MikeH]

From here you'll see that there are about 21,000 candidates per 1M n remaining.

210967 candidates for n = 10-20 million.

[vjs]

Also for sieving, p is about 1000T.

And we were getting about 20 factors in the 1K<n<20M range for every 1T sieved before the removal of k=4847.

Considering k=4847 accounted for about 13%. One could guess that we should now find ~9 factors per 1T sieved for those n 10M<n<20M.

Hope this helps.

[Greenbank]

87% * 20 = 9 ?

Up around 940T I was (9k's) seeing ~20 factors per 500G, or ~40 factors per T.

So I'd guess it's about: 87% * ~3540 = ~35 factors per T (8k's).

[ EDIT ]

Ah, but I'm counting n < 50M. Looking at the sieving scores page (which only lists n < 20M) I've found 119 factors in the 7.548T above 900T.

This works out at ~16 factors per T for 900T < p < 1000T and n < 20M.

[vjs]

Right and Phil only asked for those between 10M and 20M. So half your 16 to 8.

I say 9 we are pretty close...

I'm also going to report another average when I finish my ~8T range around 1120T, this way we know what to look forward to.

[EDIT]
Distribution per k

10223 0.1716
19249 0.0625
21181 0.1468
22699 0.0601
24737 0.1551
33661 0.1462
55459 0.2055
67607 0.0522


Distribution per k

55459 0.2055
10223 0.1716
24737 0.1551
21181 0.1468
33661 0.1462
19249 0.0625
22699 0.0601
67607 0.0522

[Greenbank]

Doh. Of course. Sorry.

[vjs]

Nope no problem I often make mistakes and I'm glad someone is paying attention and doublechecking my posts.

[philmoore]

I checked the GIMPS status page and see that about 62.5% of candidates were successfully factored in the range 10M - 20M, so that translates into roughly 226,000 candidates that required LL tests. So 210,000 or so tests for SoB in the same range means that, for the first time, SoB density of testing candidates is falling below GIMPS. It will get even better when 55459 gets eliminated, as this monster now accounts for about 21% of all tests. I'm sure this one must be on the top of Louie and Dave's hit list!