Sierp. base 6 team sieve

[mdettweiler]

Originally Posted by gd_barnes

500G-750G complete; Emailed to Anon

Reserving 1500G-1750G.

Anon, I think I'll use KriZp's P-rate/sec and your LLR speed here for optimum sieve depth calculations.

Can you LLR a candidate at n=135K and at n=170K sometime today? We can then decide whether we want to break off n=100K-150K or n=100K-200K.

KriZp, what is your P-rate/sec at P=1200G?

Using the fastest siever and a fast LLRer will be more accurate. The optimum depth will be deeper than calculating it using a slower machine but we'll get there faster so the total time spent sieving should be only slightly longer but will save much more time LLRing.


Gary

Okay, I'll be sure to do that ASAP.

[mdettweiler]

New sieve file available, sieved to a depth of p=1T (1000G). You can get it here.

[mdettweiler]

Okay, here are my timings for PRPing two test candidates at n=135K and n=170K respectively:

124221*6^135003+1 is not prime.  RES64: 7A0C21629EA30E82.  OLD64: 6E246427DBE92B83  Time: 876.532 sec.
51255*6^170000+1 is not prime.  RES64: B70F935942F0540A.  OLD64: 252EBA0BC8D0FC1A  Time: 1316.149 sec.

[gd_barnes]

Originally Posted by Anonymous

Okay, here are my timings for PRPing two test candidates at n=135K and n=170K respectively:

124221*6^135003+1 is not prime.  RES64: 7A0C21629EA30E82.  OLD64: 6E246427DBE92B83  Time: 876.532 sec.
51255*6^170000+1 is not prime.  RES64: B70F935942F0540A.  OLD64: 252EBA0BC8D0FC1A  Time: 1316.149 sec.

Whew! Ugly! Thanks for doing that.

So...LOTs of sieving to go. I think it makes sense to break off n=100K-150K with that big of a difference in LLR times.

Now, with a more educated guess, with KripZp at an est. removal rate of 129 secs/factor at P=1.3T, for the n=100K-150K range, optimum would be 1.3T * 877 / 129 ~= 8.8T. Since the removal rate is not linear in it's reduction as we remove factors, I'd round down to say optimum will be P=7.5-8T for breaking off n=100K-150K.

I'll do a more exact calculation a little later this evening.

The optimum is much higher than usual because we're sieving a large n-range, using a speedy siever here, and of course it's a non-power-of-2 base.

This shows that people can go ahead and start reserving P=500G chunks if they want to. I'll add 2 cores to this effort on Wed. or Thurs. for a total of 4 and will start reserving P=500G chunks at that point.

We'll see if we can at least knock out n=100K-150K before the Sierp base 6 server runs dry. With Beyond on it, I think I'm going to pull my 2 cores off of it later today or tomorrow and put them where they can be better utilized.


Gary

[mdettweiler]

Using the formula "current depth * LLR time / removal rate = optimal depth" with KriZp's sieve timings and my PRP timings, I got the following optimal depth when using my n=135K test candidate:

1320G * 876.532 / 125 = 9256G

For the n=170K test candidate:

1320G * 1316.149 / 125 = 13899G

Obviously, we have our work cut out for us.

[mdettweiler]

Reserving 1750G-1800G.

[gd_barnes]

Originally Posted by Anonymous

Using the formula "current depth * LLR time / removal rate = optimal depth" with KriZp's sieve timings and my PRP timings, I got the following optimal depth when using my n=135K test candidate:

1320G * 876.532 / 125 = 9256G

For the n=170K test candidate:

1320G * 1316.149 / 125 = 13899G

Obviously, we have our work cut out for us.

See my prior analysis above. It's probably closer to P=7.5T-8T for the n=100K-150K range since the removal rate reduction is not linear as we progress upward and the true removal rate is 129 / sec.

In getting the true removal rate, we use the rate based on the expected number of factors as opposed to the actual number of factors. The expected is a straight calculation and doesn't vary. The actual can vary quite a bit from what it should be.

We'll definitely want to break off the smaller range of n=100K-150K to have a chance of completing a portion of it before the server runs dry and the fact that the timing difference between n=135K and n=170K is so great. We could even do n=100K-125K or 100K-130K but it becomes too much of a hassle at such small increments until the n-values become very high.


Gary

[mdettweiler]

Originally Posted by gd_barnes

See my prior analysis above. It's probably closer to P=7.5T-8T for the n=100K-150K range since the removal rate reduction is not linear as we progress upward and the true removal rate is 129 / sec.

In getting the true removal rate, we use the rate based on the expected number of factors as opposed to the actual number of factors. The expected is a straight calculation and doesn't vary. The actual can vary quite a bit from what it should be.

We'll definitely want to break off the smaller range of n=100K-150K to have a chance of completing a portion of it before the server runs dry and the fact that the timing difference between n=135K and n=170K is so great. We could even do n=100K-125K or 100K-130K but it becomes too much of a hassle at such small increments until the n-values become very high.


Gary

Ah, I see. Okay, I guess it's probably more close to 7.5-8T then.

Either way, though, we still have plenty of work ahead of us--I've decided to put one core on this effort steadily for a while. Thus, I'll reserve 1800G-2000G too.

[em99010pepe]

Originally Posted by Anonymous

Okay, here are my timings for PRPing two test candidates at n=135K and n=170K respectively:

124221*6^135003+1 is not prime.  RES64: 7A0C21629EA30E82.  OLD64: 6E246427DBE92B83  Time: 876.532 sec.

Mine:

124221*6^135003+1 is not prime.  RES64: 7A0C21629EA30E82.  OLD64: 6E246427DBE92B83  Time: 613.748 sec.

[tnerual]

1000-1200 done (sending results just after posting this message)

reserving 2000-2500 (5 day of work)

[gd_barnes]

Originally Posted by em99010pepe

Mine:

124221*6^135003+1 is not prime.  RES64: 7A0C21629EA30E82.  OLD64: 6E246427DBE92B83  Time: 613.748 sec.

Anon, I suppose if we are using the fastest siever, we should use the fastest LLRer to compute the optimum depth. Carlos's and Karsten's quad(s) are the fastest LLRing machines that I've seen.

Using Carlos's time will reduce optimum depth for breaking off n=100K-150K. It would now be:

1.3T * 614 / 129 ~= 6.2T.

So...round down to P=~5.5T-6T to allow for future factor removal additionally reducing the sieving removal rate.

This is still only a 'ball park' estimate. When we hit about P=4T and have all factors removed to that point, then I would consider the factor removal rate at that point close enough to extrapolate an optimum sieve depth.

Then, we'll get to do it all over again for n=150K-200K starting from P=~5.5T-6T.

If anyone has a faster sieving or LLRing machine -AND- you will be either helping with sieving or LLRing Sierp base 6 now or in the future, let me know. I want to get as close as possible to an apples-to-apples comparison.


Thanks,
Gary