Reserved for MF - Sequence 3366

[firejuggler]

starting a polyselect for 3366.i2070

[firejuggler]

Got a pretty close one early

R0: -131814849686543684690287283
R1: 6033142268549
A0: 13291547623250508786464108895384
A1: -390461045924957707581438242
A2: -22443904701664381846805
A3: 11962516130649978
A4: 6305096952
A5: 108
skew 1676515.02, size 8.687e-013, alpha -6.968, combined = 5.540e-011 rroots = 5
expecting poly E from 5.75e-011 to > 6.62e-011

[EdH]

Originally Posted by VBCurtis

...

Edit: or was this just for fun?

Actually, I'm just starting my machines back up after a long break and can't remember how I ran some of my scripts. With all my machines running, I could have knocked off the c121 in just a few hours. But, I haven't had the time to jump back in and YAFU won't accept externally generated relations without a restart, which I haven't worked out yet. So, it was simple to just do some ECM "just for fun" and I got lucky with some factors.

After I get some more time and figure out my scripts (or, write some new ones), I'll get back into it a little more efficiently.

The 2000 curves was just due to laziness and the up-arrow in my terminal.

Thanks for all the info.

[EdH]

Sorry firejuggler...

via YAFU:

pm1: starting B1 = 15M, B2 = gmp-ecm default on C133
ecm: 904/904 curves on C133, B1=1M, B2=gmp-ecm default, ETA: 4 sec    
ecm: 2350/2350 curves on C133, B1=3M, B2=gmp-ecm default, ETA: 12 sec   
ecm: 58/266 curves on C133, B1=11M, B2=gmp-ecm default, ETA: 1.28 hrs 
Total factoring time = 18088.3234 seconds


***factors found***

P43 = 9312963830713538916612432739005058910946781
P90 = 461486173109338394831862317697747675929519312519625762993004868463115580276796633827691823

[RichD]

-pm1 2e9 - nothing

[henryzz]

Originally Posted by VBCurtis

In this case, it worked nicely and saved you time! While B1 = 3e6 is the "right" choice for a t40, I find that using 11e6 costs little extra time for the t40 level, while increasing my chances of a factor the size you found (p45) pretty substantially. Even doing 250 43e6 curves is a t40, though a B1 that big would cost a fair amount more time for a t40 than a smaller choice. In fact, I've been meaning to sample a bunch of B1s to see which choice minimizes the time to complete a t45- I've done a few experiments before, and 11e6 is not optimal on my machines with gmp-ecm 6.4.

Edit: or was this just for fun?

I agree with this logic. I think we in general focus too much on doing a particular digit level rather than maximizing the chance of finding a factor.

Another thing to watch out for is on my pc running with -B2scale 0.5 produces quite a boost. Also with the new 7.0 beta it chooses the wrong parameterization. By default it is -param 1, -param 2 is best for me.
Testing on the c133 4297804038541675450291447604994914895907145266366160553241655511889823941847458209864972187113512067175152346676676239212308821871763

35      40       %40     options
1.99h   19.07h   10.4     1e6
1.83h   17.80h   10.3     -B2scale 0.5 1e6
1.63h   15.73h   10.3     -B2scale 0.5 -param 2 1e6
1.64h   12.14h   13.5     -B2scale 0.4 -param 2 3e6
2.14h   12.32h   17.4     -B2scale 0.3 -param 2 11e6
2.13h   12.08h   17.6     -B2scale 0.5 -k 2 -param 2 11e6

On my system it looks like -B2scale 0.4 -param 2 3e6 probably wins for if you are doing t35. It would possibly be worth running something like 5e6 sacrificing 10-20% speed in order to get more chance of larger factors.

Another way of doing it would be to set a time limit say min+10% or whatever. I will use 2h in this example. You would work out approximately how many curves at 3e6 and 11e6 you can run in 2h maximizing the chance of finding larger factors(by running as many at 11e6 as possible).

It is an interesting problem. I would very much recommend looking at optimizing the parameters above. I got down from 1.99h to 1.63h at no cost to the %40 at all above. I then sacrificed a small amount of time to raise the %40 a fair bit. That looks like it is definitely worth it to me. I would be interested in your experiments down the same line for higher levels.
There is of course the fact that it is fun to find the larger factors as well.

[RichD]

2130 @ 3e6 - nothing.

...pausing...

[EdH]

GMP-ECM 6.4.4 [configured with GMP 5.1.1, --enable-asm-redc] [ECM]
Using B1=43000000, B2=240490660426, polynomial Dickson(12), 2 threads
Done 1401/2000; avg s/curve: stg1 124.7s, stg2 43.49s; runtime: 21579s

Run 1401 out of 2000:
Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=3868230208
Step 1 took 126859ms
Step 2 took 42661ms
********** Factor found in step 2: 18355806065973123350521061540546697152380645256413569539
Found probable prime factor of 56 digits: 18355806065973123350521061540546697152380645256413569539
Probable prime cofactor 1714861771731971184242809368426752003463034552779770056154504837499622621019685277733403523 has 91 digits

[VBCurtis]

Henry-
I have run a substantial number of B1/B2 variations to find the best setup on ECM 6.4. My setup for the experiments: i7-740, 8GB. 2xLLR (exponents 1.5M, memory bus not saturated), 1xECM (43m) also running. I ran B1 at 1M increments from 2M to 21M, and a variety of B2 for the interesting B1.

I recorded stage-1 time to make sure no background process influenced the timings. Under these conditions, stage 1 took just under 8 sec per 1M of B1. I reran curves that did not 'fit'. Table attached below.

The fastest t40 happened at B1=5e6, B2=8.5e9. 1494 curves for t40, 11523 for t45.
2.5 minutes behind is B1=6e6, B2=8.5e9. 1323 curves for t40, 9880 for t45.
At default B2, the winning B1 is 4e6, because it uses 8.5e9 as default B2. This is 7 min slower than the best setting. 1755 curves for t40, 14170 for t45.
Default 3e6/5.7e9 is approx 45 min slower, or 3%.

If we instead go for Henry's idea of maximizing larger factor chances without giving up much time on this level, we can get the same (within 1% error) t40-time as default settings by using B1=12e6, B2=23e9. This has 697 curves for a t40, and 4540 curves for a t45, and is 3% slower than the best t40 setting. No higher B1 is within 5% of optimal settings, so the time saved on higher factors is not worth it while targeting a t40- though it clearly is for these settings.

Conclusion: When running a t40, use B1=12e6, B2=23e9.
I learned that the fastest times happen when k=2 or k=3. See data sheet for details. I will continue this experiment for optimal t45 settings overnight.
-Curtis

[VBCurtis]

I haven't put the spreadsheet into organized form yet, but the optimal B1/B2 on my machine for a t45 is 19e6/96e9, 2526 curves. This is 6.58 days, versus default 11e6 at 6.80 days. About 3.5% savings, or 5 hours.

At default B2, B1=34M is the highest B1 with t45 time equal to the default 11M. It happens to also be nearly the same time for t50 as B1=43M, thanks to a more efficient k=3 setting for B2 (144e9).

I have not done experiments with B2 settings for B1 above 30M; once I do, I'll post the data sheet. It is possible that B1 in the 35-40M range with B2 fixed at 144e9 will also be the same time for t45 as 11e6.

-Curtis

[EdH]

Run 831 out of 2000:
Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=2007158222
Step 1 took 122671ms
Step 2 took 42034ms
********** Factor found in step 2: 9027806517589529957426159256933280612412291325241
Found probable prime factor of 49 digits: 9027806517589529957426159256933280612412291325241
Probable prime cofactor 281266226834456319808816318260329168307503549157181457839582869005693367645821260664942051 has 90 digits