Sieving discussion thread

[gribozavr]

It means that +1 number has a small factor, thus NewPGen deleted the k (because we want both -1 and +1 to have no small factors).

[cipher]

n=500,000
range= 0-50G
sieving depth= 426.3 T (Target 500T for Release Approx Apr 1'07)
candidates= 18,344,289
Avg K per 1M = 367

[cipher]

n=500,000
range= 0-50G
sieving depth= 520.7
candidates= 18,128,550
Avg K per 1M = 363

[Joshua2]

I've got a core 2 duo with 2gb of ram, and I would be interested in doing seiving for n=500,000 but I would want to do cipher and moomoo's range, both with high depth, because I have so much memory.

[MooMoo2]

There is a ~1200T difference between cipher's range and my range, so combining them will not be possible now. I still prefer to leave the sieving separately (1-50G and 50-208G), since 50G-208G will be very close to or at the optimal sieve depth once 1-50G is completed by PrimeGrid (which would happen about 3 years from now, assuming PG's participation increases by 50%, and that we find the n=333,333 twin tomorrow).

Also, a 50G sieve file means more people would be able to join TPS, since the RAM requirements are lower.

[KEP]

Originally Posted by MooooMoo

There is a ~1200T difference between cipher's range and my range, so combining them will not be possible now. I still prefer to leave the sieving separately (1-50G and 50-208G), since 50G-208G will be very close to or at the optimal sieve depth once 1-50G is completed by PrimeGrid (which would happen about 3 years from now, assuming PG's participation increases by 50%, and that we find the n=333,333 twin tomorrow).

Also, a 50G sieve file means more people would be able to join TPS, since the RAM requirements are lower.

MooooMoo what is the optimal sieving depth for the n=500,000 range? Can you tell me how to generally find the optimal sieving depth for any n? Since I'm doing my own prime research at the moment and propably for the next decade, I'll wish you all good luck and good will, since I'm not able to participate any further and for the next long time beeing :)

[MooMoo2]

The optimal sieving depth for n=500,000 is between 50P and 200P (it depends on your PC. Pentium 4's have a lower optimal sieving depth than athlons).

As a rough guide, the optimal sieving depth increases by a factor of 16 for every doubling in the size of the exponent. For example, the optimal sieving depth for n=666,666 will be ~16 times as great as the optimal sieving depth for n=333,333.

[gribozavr]

Optimal sieving depth is reached when sieving removes k's at the same rate as LLR. But You should start LLR a bit earlier, because (quoting someone from mersenneforum) "the goal is to find primes, after all".

[biwema]

Originally Posted by MooooMoo

I still prefer to leave the sieving separately (1-50G and 50-208G), since 50G-208G will be very close to or at the optimal sieve depth once 1-50G is completed by PrimeGrid (which would happen about 3 years from now, assuming PG's participation increases by 50%, and that we find the n=333,333 twin tomorrow).

Please group these 2 subranges together. The sieving will not slow down and the memory requirement is not that large anymore since the nuber of k is permanently dropping. Furthermore you will get a higher and better optimal sieving point when sieved together. When sieved seperately, the efficiency of sieving is only half as good.


A little bit off topic:
I have the feeling that we should rethink the credit system of the sieving effort. Now that person who did the most sieving will get also credit of the twin prime find. The result now is, that many people try to start sieving their own N (sometimes even beyond 500000) or their own range in a k (what makes mathematically absolutely no sense).
It seems as if one person gets the credit, if a N=500000 twin is found at 0-50G and someone else if the twin is between 50G and 206G. Both of these 2 people spend the same amount of cpu time in sieving as if they sieve the whole range alone.
If some people see that they have no chance of doing the most effort, they may also move to some other task.
Also constellations like lucky plus or minus are forgotten.

I suggest not specially crediting one person for sieving (like gimps itself). It is not fair either, but will concentrate the sieving effort on the current and next candidate only.

biwema

(from tomorrow I will have very limited internet access for one month (holidays). I will read replies later.)

[MooMoo2]

Now that person who did the most sieving will get also credit of the twin prime find. result now is, that many people try to start sieving their own N (sometimes even beyond 500000)

I don't know of anyone in TPS trying to sieve any other n besides n=333,333 and 500,000.

Originally Posted by biwema

If some people see that they have no chance of doing the most effort, they may also move to some other task.

One of the reasons for crediting the siever is to bring more people into sieving. If people see that no one is getting credit for sieving (but the top producer does gets credit for LLR tests), then very few people will bother to sieve because of these reasons and because there is no chance of getting the glory of finding primes. This is important, since the n=333,333 range is already undersieved.

Also, giving credit to the top producer for sieving increases the sieving rate by keeping top producers from "slacking off". For example, Skligmund is currently the top producer and has no ranges in progress. If he wants to maintain his position, he'll have to continue sieving as soon as others start catching up.

I suggest not specially crediting one person for sieving (like gimps itself). It is not fair either, but will concentrate the sieving effort on the current and next candidate only.

That's basically what we're doing now. We haven't chosen the next n yet, so sieving has to take place on either n=333,333 or n=500,000. Participants aren't allowed to sieve other n (they can, but it's likely that n won't be used. Even if it is used, they'll get 0 credit for it.)

---------------------------------

In regards to merging the files, I've decided to keep them separate because it's the lesser of two evils.

Case 1: Keep the 1-50G and 50G-208G files separate.
- TPS's current sieving rate is about 25T per day. Let's say that participation remains the same. In that case, sieving on 1-50G will progress at about 25T per day.
- After 1-50G is done, 50G-208G will be very close to or at the optimal sieve depth.

Case 2: Merge the 1-208G files.
- Fewer people will be able to meet the RAM requirements, which are over 4 times as great as the RAM requirements for 1-50G. I don't know exactly what the effect will be, but 1-50G will progress at a slower rate than 25T.
- After 1-50G is done, 50G-208G may or may not be near or at the optimal sieve depth.

[Joshua2]

Right, I think the top seiver must receive credit, otherwise seiving will not reach anywhere near optimal levels. I think case 2 is better, because I think most of us have enough ram. 25T per day is what we want, and I seive about 19T per day. I'm sure somebody can seive 6T a day.