Factor bragging

[hc_grove]

This one isn't as smooth as the one I found earlier this month, but still pretty smooth:

4506302931860941 | 19249*2^10139378+1
4506302931860940 = 2^2*3*5*7*73*199*293*911*2767

[Greenbank]

Secondpass...half way through the range on B1=B2=20000. Will up this depending on the rate of double-check tests.

1393019896005342 | 24737*2^4351903+1

(p just over 2^50)

p-1 = 2 * 3^2 * 11 * 167 * 557 * 5399 * 14009

[garo]

I got a big one this morning:

104061448755062288629 | 10223*2^3927977+1

BTW, can someone check their logs and tell me how much time a current doublepass PRP takes on a P4. Also let me know the speed of your machine.
Thanks.

[Greenbank]

Nice.

n=3870847 took 15 hours on a P4 3.0GHz running Linux
n=3876754 took 15 hours on a 3.0GHz Xeon running Win2k Server.

[DigitalConcepts]

Originally posted by garo
104061448755062288629 | 10223*2^3927977+1

p-1 = 2^2 x 3 x 109 x 173 x 643 x 4177 x 6217 x 27541

[vjs]

Garo,

What's your success rate using the small bounds. And do you think it's worth the effort to P-1 the unfactored ranges? If so I'll start a new thread for those n 4M<n<5M that are previously untested.

At the rate we are proceeding with these doublechecks, ~1K tests per day and less than <21K between 4M<n<5M. I have a feeling we will double check out to at least 5M fairly soon, even if the firstpass que is populated.

[garo]

On my 2.6GHz the PRP should be taking about 900*3000/2600 = 1038 min or 17hr 18min. I tried P-1 with Pfactor with sieve depth being the correct 49.7. The lowest factor value for which Prime95 worked was 2.7 which gave me bounds of B1=20k and B2=165K. With these bounds the chance of finding a factor was 0.435 and the test took about 620 seconds. Hence P-1 was saving one test every 2375 minutes.

Hence we can conclude that:

1) P-1 is not worth it. You can do a test in half the time it takes to find a factor.
2) Prime95's calculation is accurate and when it says no point doing P-1 factoring, there really is no point doing P-1 factoring.

[hc_grove]

This one is smoother than your average factor:
18628509020177411 | 67607*2^10629251+1
18628509020177410 = 2*5*17*1297*1601*6553*8053

[vjs]

Not bad HC... not bad at all. The smoothest factor was found by sieve above post.

But yours certainly ranks in the smoothest I've seen for P-1 thus far.

[hc_grove]

Originally posted by vjs
Not bad HC... not bad at all. The smoothest factor was found by sieve above post.

But yours certainly ranks in the smoothest I've seen for P-1 thus far.

The smoothest I've found by P-1 is:
268260631411561 | 10223*2^5240741+1
268260631411560=2^3*3*5*101*241*293*463*677

Back in the early days of P-1 mklasson found:
40315798264717 | 21181*2^4031084+1
40315798264716=2^2*3^3*13*211*367*601*617

[Nuri]

Both cool...

[vjs]

Those are certainly impressive.

[Greenbank]

Hurrah, after weeks of nothing from P-1 I finally get one at 6:47am on New Years Day.

7233758839303943 | 24737*2^10645207+1

P-1 = 2 * 11 * 29 * 97 * 271 * 2333 * 184879

[Greenbank]

1058699706255400291 | 33661*2^10649232+1

p-1 = 2 * 3 * 5 * 29 * 193 * 7607 * 28549 * 29033

[MikeH]

Just found with ECM @ 25 digits

6112285295043972389 | 67607*2^7691+1

which was the 4th smallest unfactored n for k=67607

[Greenbank]

I'm doing P-1 on 200000 to 250000 but I just submitted these factors:-

110339071626803 | 33661*2^224160+1
4802938257372379 | 55459*2^228718+1
3068443382948634853 | 21181*2^231548+1

without logging in. Should be assigned to user 8141. Ta.

[MikeH]

ECM found a factor in curve #3, stage #2
Sigma=5670788764645674, B1=7400, B2=740000.
10223*2^96221+1 has a factor: 278687290515007924794729914252113

33 digits. And ECM reports it as being prime. Biggest for us this year.

[Greenbank]

ECM found a factor in curve #3, stage #2
Sigma=5670788764645674, B1=7400, B2=740000.
10223*2^96221+1 has a factor: 278687290515007924794729914252113

33 digits. And ECM reports it as being prime. Biggest for us this year.

Good work but I'm afraid it is composite:-

642379309914469 x 433836031475102077

[MikeH]

Good work but I'm afraid it is composite:-

642379309914469 x 433836031475102077

Ahh. Must check my ECM settings for primality testing.

[Greenbank]

If it's under 2^64 then I use the linux command line program 'factor'.

If it's bigger than 2^64 then I just stick it through Alpetron's applet: http://www.alpertron.com.ar/ECM.HTM

[MikeH]

Thanks for the link. Very useful and interesting.

[Greenbank]

3617343986912807923736443 | 67607*2^202131+1

p-1 = 2 * 3^2 * 71 * 263 * 9209 * 11383 * 90847 * 1130117

B1=1M B2=100M

[Keroberts1]

you realize that by raising the B1 by 131K yo ucould have found it without performing stage 2

[DigitalConcepts]

you realize that by raising the B1 by 131K you could have found it without performing stage 2

How much time (percentage) would it have saved?

Which would have been better?
Raising B1 by 131K, or lowering B1/B2 by a factor of 10?

[Greenbank]

But how would I have known to do that?

You've got to set bounds without knowing what the factors will look like.

[Nuri]

If I'm not mistaken, Prime95 suggests a B2/B1 ratio of around 20 for B1 values at 1,000,000.

[vjs]

Yup that's always the point...

One could also say, you could have simply taken the number

67607*2^202131+1

and divided it by

3617343986912807923736443

Seriously though, what were your memory requirements like for the stage2 portion. Also time to complete for each stage, a 1:100 ratio for B1:B2 seems a little high but it works.

Are you doing stage two with prime95 have they married the two clients yet.

[Greenbank]

It was a windows box that wasn't networked and that I would only visit once a week or so. So I wanted to give it a big chunk of work without worrying about it, hence the large bounds.

[MikeH]

[Fri Feb 24 07:35:05 2006]
ECM found a factor in curve #80, stage #2
Sigma=4857056233298550, B1=250000, B2=25000000.
33661*2^5112+1 has a factor: 1462205790618779672559199619

28 digits. 6th smallest n for that k. And it realy is prime this time.

[KWSN_Dagger]

[Sat May 13 01:18:10 2006]
P-1 found a factor in stage #2, B1=70000, B2=822500.
24737*2^11050087+1 has a factor: 594262015630211281

p-1= 2 ^ 4 x 3 x 5 x 11 x 17093 x 54449 x 241861

2^4??

And of course it has to be a composite.

[SlicerAce]

[Fri Oct 26 22:49:45 2007]
P-1 found a factor in stage #2, B1=130000, B2=2200000.
55459*2^15009238+1 has a factor: 5155366181720738537

and the factor is prime

[Kman1293]

[Fri Dec 14 17:07:25 2007]
ECM found a factor in curve #2260, stage #1
Sigma=7131277753749641, B1=3000000, B2=300000000.
10223*2^1181+1 has a factor: 2869295942753555058435842630879466239475749080003

The factor is prime.

49 digits long.

[vjs]

Wow that is actually quite the find!!! Well done.

Did you check to see if the residual is prime or not? ( nope it's composite) I would say probably not prime but it would be interesting to know.

P-1 = 2 x 3 ^ 2 x 23 x 189661 x 39 361343 990616 327487 x 928 382719 429012 307749
P+1 = 2 ^ 2 x 40037 x 106 442681 x 4 343431 551583 x 38752 974121 352341 178651

Nice....

[Kman1293]

11878266738982198597668979 | 10223*2^39449+1
6650798327357434873224599831 | 10223*2^10757+1
650124655703350600814106133 | 10223*2^15437+1
9419400746144284880591 | 10223*2^41285+1
4380505951119731733855769913 | 10223*2^17477+1
13217355082313000541253 | 10223*2^42797+1

Theres a few more factors that my machine found overnight. They've all been verified and submitted.

On the 49 digit factor I haven't done any tests with the residual other than just testing to see if the factor was prime or not.