Factor bragging

[jjjjL]

We should have a small thread here dedicated to showing off our discoveries as they come in. They don't belong in the coordination thread and they don't really belong in the client thread either.

So to get the boasting started, here's my latest factor:

276504238660693 | 27653*2^5522829+1

276504238660693-1 = 2 ^ 2 x 3 x 7 x 43 x 577 x 877 x 151279

Just found it. Good thing too considering the next assignment is currently 10223*2^5518457+1. Living on the edge. :D

Cheers,
Louie

[dmbrubac]

I found

1328735974435881607 | 22699*2^5627854+1 a few days ago and
28195479692754961 | 67607*2^5635211+1 just now.

BTW how do you figure out how the factor expands like that? What makes one smooth and another not? (Hey, I'm not a math guy - so what!)

[hc_grove]

Originally posted by dmbrubac
1328735974435881607 | 22699*2^5627854+1 a few days ago and
28195479692754961 | 67607*2^5635211+1 just now.

BTW how do you figure out how the factor expands like that? What makes one smooth and another not? (Hey, I'm not a math guy - so what!)

I normally use the ifactor function in Maple, for your factors I find:
28195479692754961-1=2^4*3*5*37*41*179*7213*59981
1328735974435881607-1=2*3^2*7^2*17*449*541*11083*32917

These numbers are so small that factoring them is no problem at all (trial division is probably a bad idea though), so you can use almost any program that can handle the numbers. I believe Louie once told what he uses in the 'P-1 factorer' thread.

Smooth just means that all the factors are small. I wouldn't call either of those factors smooth.

[jjjjL]

Originally posted by hc_grove
I believe Louie once told what he uses in the 'P-1 factorer' thread.

Yeah, I use an online java applet at http://www.alpertron.com.ar/ECM.HTM

It's probably overkill for these sized numbers but it's easy to use and if I'm away from my main computer, I can just search google for "ecm java factor" and find it real easily.

So just subtract 1 from your factor, put it in the top text box, and press enter. It will factor the number into it's prime components in a fraction of a second.

Cheers,
Louie

[hc_grove]

Originally posted by hc_grove
These numbers are so small that factoring them is no problem at all (trial division is probably a bad idea though),

I was wrong, I just coded up a quick trialfactorer and it factors both your numbers and Louie's so fast the time command can't measure it (on my 2GHz laptop that does regular factoring in the background).

You can download a UNIX version of the program (called trial) and the source code (trial.c) here (http://www.sslug.dk/~grove/sbfactor/) (the same place as where you can get my version of the factorer).

You can give the program either p or p-1 as input it will figure that out.

It only works with numbers < 2^64.

[Mystwalker]

Just found:
2186703185472067 | 10223*2^5595929+1 :bouncy:

2186703185472067-1 = 2 x 3 x 157 x 907 x 22639 x 113051

[hc_grove]

I just found:
176963110569601 | 28433*2^5691433+1

Unfortunately I found that factor 4 days ago sieving :( I need to update my results.txt.

The factorization of P-1: 2^7*3*5^2*151*1367*89303

2^7 isn't something we see every day.

[Mystwalker]

Got another one:

62447276586432949 | 28433*2^5598025+1

62447276586432949 - 1 = 2 ^ 2 x 3 x 7 ^ 3 x 17 x 29 x 31 x 15107 x 65713

[hc_grove]

My two newest factors:

677309463913963 | 24737*2^5705071+1
782666928978908543 | 27653*2^5705673+1

677309463913962 = 2*3*11^2*2477*12161*30971
782666928978908542 = 2*19^2*43*97*443*10037*58451

[Mystwalker]

323790238554919 | 24737*2^5599951+1

323790238554918 = 2 x 3 x 251 x 991 x 1609 x 134837

[hc_grove]

295288546740041 | 27653*2^5693433+1

295288546740040 = 2^3*5*7*17*73*12211*69593

[hc_grove]

Once again I found a factor that was already known :(

19144825376419 | 10223*2^5694269+1

This time the factor is to new to be in results.txt so it would even have helped me to update that (it was a week old so it was about time)

19144825376418 = 2*3^3*7*43*59*1021*19553

[dmbrubac]

32089592427168210307 | 67607*2^5664627+1
=2 * 3 * 241 * 1033 * 13627 * 24103 * 65407

13860049223357177 | 55459*2^5720278+1
=2^3 * 7 * 823 * 1361 * 1657 * 133351

[Nuri]

Originally posted by hc_grove
Once again I found a factor that was already known :(

19144825376419 | 10223*2^5694269+1

This time the factor is to new to be in results.txt so it would even have helped me to update that (it was a week old so it was about time)

19144825376418 = 2*3^3*7*43*59*1021*19553

That's strange...

This factor was submitted in April 2003 (notice it's a 19T factor).

[jjjjL]

yeah, that should value shouldn't even be in the current .dat file. yours must be old.

[hc_grove]

Originally posted by jjjjL
yeah, that should value shouldn't even be in the current .dat file. yours must be old.

I've replaced it with the one I've used for sieving since we started sieving n=1M to 20M.

[hc_grove]

This time an unknown factor: :)

6853123410953119 | 4847*2^5707551+1

6853123410953118 = 2*3*13*17*9403*12227*44953

[Frodo42]

finally I'm back in the race with a factor

58266879992975447 | 27653*2^5713017+1
58266879992975446 = 2 x 13 x 509 x 10007 x 16231 x 27107

I was getting woried that I would not find anything anymore, but I guess its my turn for some bad luck, or maybe it's because I'm only using half the CPU of I have used the last couple of months since a working prp-client for this Linux-box appeared.

[Frodo42]

Yiekes I have also started finding factor-duplicates with P-1
18197867605331 | 55459*2^5713714+1
I guess it's time to change from 47 to 48 ...

Weird it's nowhere to be found in the result.txt file, is this one also to old to be in the SoB.dat?

[MikeH]

Weird it's nowhere to be found in the result.txt file That's 'cause it's too small. At 18T it's in the lowresults.txt file.

You need the latest sob.dat file from which all these canidates are removed, then the latest results.txt file will work fine.;)

latest sob.dat (http://www.aooq73.dsl.pipex.com/SobDat_n1M-20M.zip)

[Frodo42]

That's 'cause it's too small. At 18T it's in the lowresults.txt file.
Thanks, I hope I haven't wasted too much CPU rechecking small factors ...

[priwo]

210713652400249 | 33661*2^5737128+1
210713652400248-1 = 2 ^ 3 x 3 ^ 2 x 19 x 541 x 284 714321

210718454330387 | 21181*2^5740772+1
210718454330387-1 = 2 x 2371 x 44436 620483

both found today with the sieve

[Nuri]

762210304266563 | 27653*2^5992989+1

762210304266562 = 2 x 281 x 2797 x 9871 x 49123


I've recently finished two 8000 ranges, and this is the only factor I got out of the 467 k/n pairs within the 16000 range.

So, the question is, do you think this is normal? (I mean, 0.2% hit rate)

PS: May be, it has something to do with the settings I use (48 1.3 160).

[hc_grove]

Just found a new factor:
223648654756363 | 10223*2^5709401+1

223648654756362 = 2*3*11^2*1231*7757*32261

Mystwalker is going to (or might have, but just not reported) find this factor sieving within the next days. As Mystwalker is the next to pass on the scoreboard, this couldn't be better. :|party|:

[Mystwalker]

Originally posted by Nuri
I've recently finished two 8000 ranges, and this is the only factor I got out of the 467 k/n pairs within the 16000 range.

So, the question is, do you think this is normal? (I mean, 0.2% hit rate)

PS: May be, it has something to do with the settings I use (48 1.3 160).

I also got very few factors lately (none in the last ~7000), although I'm using B1=35000, B2=411250. :(



Originally posted by hc_grove
Just found a new factor:
223648654756363 | 10223*2^5709401+1

223648654756362 = 2*3*11^2*1231*7757*32261

Mystwalker is going to (or might have, but just not reported) find this factor sieving within the next days.

I'm not that far right now. Chances are that PRP will get there first (well, second ;))...


As Mystwalker is the next to pass on the scoreboard, this couldn't be better. :|party|:

That should still take some months. Plus, I still got a neat trick or two left once I have enough time to accomplish them. :D

[hc_grove]

And once again a new factor

780376430289319 | 10223*2^5733485+1

780376430289318 = 2*3*29*2617*10091*169831

[Mystwalker]

The whole time nothing and then ... 2 ones right after each other! :elephant:

819201694820819 | 27653*2^5737929+1
819201694820818 = 2 x 239 x 479 x 32251 x 110939

520550137161211 | 33661*2^5738184+1
520550137161210 = 2 x 3 x 5 x 13 x 41 x 439 x 2663 x 27847


What bounds are you guys using?
I'm especially interested in the B2 bound. There have been almost no p-1 factor factors (so to say...) higher than 100,000 and a little...
Maybe I should use lower bounds then.

[hc_grove]

The fifth (and final) factor:
1649427586996001 | 24737*2^5709871+1

1649427586996000 = 2^5*5^3*7*31*73*197*132137

I've used optimal bound (1.5 47 384) giving B1=25000 B2=231250.

[dmbrubac]

52252110283617819719 | 10223*2^5725757+1
52252110283617819718 = 2*11*13*281*353*5981*10711*28751

[Nuri]

Originally posted by Mystwalker
The whole time nothing and then ... 2 ones right after each other! :elephant:


2 OrkunBanuTST (Nuri) 1731196.94+(10.82) ......
3 Mystwalker 1720152.33+(10.75) .......


:scared:

I must do something, and do it quickly. ;)

[dmbrubac]

Originally posted by dmbrubac
52252110283617819719 | 10223*2^5725757+1
52252110283617819718 = 2*11*13*281*353*5981*10711*28751

This factor isn't showing up on the stats page. Any ideas why not? The submission page took it OK.

[hc_grove]

Originally posted by dmbrubac
This factor isn't showing up on the stats page. Any ideas why not? The submission page took it OK.

Probably because it's larger than 2"64 and should be submitted via http://www.seventeenorbust.com/largesieve/ to actually end up in results.txt. I think I've seen the ordinary submission form accept large factors without actiing on them before.

[dmbrubac]

Thanks!

[MikeH]

Originally posted by dmbrubac
52252110283617819719 | 10223*2^5725757+1
52252110283617819718 = 2*11*13*281*353*5981*10711*28751

There is something strange here. This factor is less than 2^64 (only just), but when I try to submit it I get


52252110283617819719 10223 5725757 verified.

Factor table setup returned 1
Test table setup returned 1

1 of 1 verified in 0.07 secs.
1 of the results were new results and saved to the database.

And I get the same no matter how many times I try.:confused: Strange, is it being added to the DB or not?

EDIT: Not a big problem, one of your attempts to submit the factor obviously worked, it's there in the stats now.:)

And that makes it the second largest factor found this year.:|party|:

[hc_grove]

Originally posted by MikeH
There is something strange here. This factor is less than 2^64 (only just), but when I try to submit it I get


18446744073709551616 = 2^64
52252110283617819719 = this factor

Which looks larger to you?





Factor table setup returned 1
Test table setup returned 1

1 of 1 verified in 0.07 secs.
1 of the results were new results and saved to the database.

And I get the same no matter how many times I try.:confused: Strange, is it being added to the DB or not?


This is exactly what I've seen with factors larger than 2^64 and the ordinary submission page.

[dmbrubac]

well, it is a factor bragging thread! :moon:

[Mystwalker]

Then let's brag again! :D

357737103943831 | 4847*2^5738943+1
357737103943830 = 2 x 3 ^ 3 x 5 x 13 x 601 x 9227 x 18379

Seems like Nuri is 3rd now. :Pokes: :p

[MikeH]

18446744073709551616 = 2^64
52252110283617819719 = this factor

Which looks larger to you? Remind me never to use Windows calculator for big math again :swear:

Paste the number in decimal, switch to binary, it's <2^64. Guess that's because WinCalc only handles math upto 2^64.:bonk:

[mklasson]

Originally posted by MikeH
Remind me never to use Windows calculator for big math again :swear:

Give http://pari.math.u-bordeaux.fr/ a try -- it's great.

[Nuri]

Seems like Nuri is 3rd now.

Another sieve factor that came just in time.

216379013870543 | 4847*2^5861391+1

[hc_grove]

3593405260603031 | 10223*2^5774585+1

3593405260603030 = 2*5*31*3187*16573*219463

[Nuri]

15799176637249321 | 4847*2^6001023+1

15799176637249320 = 2 ^ 3 x 3 ^ 2 x 5 x 7 x 47 x 1163 x 3137 x 36563

[dmbrubac]

5720000 -> 5730000 had 5 factors:

13860049223357177 | 55459*2^5720278+1
13860049223357176 = 2^3*7*823*1361*1657*133351

52252110283617819719 | 10223*2^5725757+1
see previous post

2408494707706313 | 67607*2^5726411+1
2408494707706312=2^3*353*1597*9041*59069

1990620885055391 | 21181*2^5726972+1
1990620885055390=2*5*7*41*2351*4483*65809

363916348856369 | 24737*2^5727391+1
363916348856368=2^4*7*11*19^2*14891*54949

[Nuri]

407337342926141 | 21181*2^5777180+1

407337342926140 = 2 ^ 2 x 5 x 11 x 31 x 41 ^ 2 x 59 ^ 3 x 173



Does anyone have smoother P-1? :bouncy:

[hc_grove]

Originally posted by Nuri
407337342926141 | 21181*2^5777180+1

407337342926140 = 2 ^ 2 x 5 x 11 x 31 x 41 ^ 2 x 59 ^ 3 x 173



Does anyone have smoother P-1? :bouncy:

Well you still have to have B1 >= 1681 (41^2) and B2 >= 205379 (59^3) to find that, so I don't really know if it counts as smooth.

[Nuri]

To be honest, I do not know much about the theory (or math) behind it, so I'll take your word for the concept of smoothness. (I previously thought it meant having many small prime factors for P-1).

But, there's something I do not get. I used B1=10000 and B2=65000 (That's the first k/n pair after I switched to lower settings of 1.25x and 160MB to keep up with PRP).

[hc_grove]

Originally posted by Nuri
To be honest, I do not know much about the theory (or math) behind it, so I'll take your word for the concept of smoothness. (I previously thought it meant having many small prime factors for P-1).

But, there's something I do not get. I used B1=10000 and B2=65000 (That's the first k/n pair after I switched to lower settings of 1.25x and 160MB to keep up with PRP).

Smooth means that all the factors are small. What I don't remember is whether it's 59 or 59^3 you have to consider a factor.

As for the bounds it would be possible to find the factor if the factorer doesn't only try primes (and prime powers) between B1 and B2. Whether that or something I can't think of is the explanation, we have to hear Louie about, since he's probably the only one knowing that part of the code well enough.

[prime95]

Originally posted by hc_grove
As for the bounds it would be possible to find the factor if the factorer doesn't only try primes (and prime powers) between B1 and B2. Whether that or something I can't think of is the explanation, we have to hear Louie about, since he's probably the only one knowing that part of the code well enough. [/B]

Stage 2 does drag in some composite numbers between B1 and B2. So I think stage 1 caught the 59^2 and stage 2 picked up the other 59 in a composite number between B1 and B2.

[dmbrubac]

5740000 -> 5745000 gave me

9422557846421851 | 28433*2^5741185+1
9422557846421850=2*3^9*5^2*13*17*29*89*113*108287

249632915700529 | 10223*2^5743901+1
249632915700528=2^4*3^3*1399*2027*203773

but this is real bragging

[hc_grove]

A pretty smooth factor:

322163790109561 | 19249*2^5763038+1

322163790109560 = 2^3*3^3*5*7*107*113*1637*2153

[Frodo42]

Just found a factor in a range beings fast-checked (factor value 1.2)
1172536902962371 | 19249*2^5794718+1

It seems to me that we are having trouble keeping up with PRP, and I'm being closed in by priwo if I don't find some more factors fast :geezer: I only have something like 1:15 of his factors in store so I have to keep finding P-1-factors to stay in the race.

[hc_grove]

My newest factor:

220516583040629 | 28433*2^5840545+1

220516583040628 = 2^2*7*127*1879*2113*15619

Once again, this is a factor that Mystwalker will find in his sieving range :moon:

[Nuri]

I found 233793054676939 | 4847*2^5884647+1 today through sieving.

Unfortunately, it turned out to be a duplicate of 173003399270327 | 4847*2^5884647+1.

I guess the chances of such a thing to happen is really low (i.e. ~1 out of every 5.200 factors => to find a factor through sieving that's in the active range is 200k/19m and ratio of duplicates is currently at 1.8%).

:bang: :bang: :bang: :bang: :bang:

[hc_grove]

1185354900631669 | 55459*2^5843506+1

1185354900631668 = 2^2*3*13*5557*6949*196771

[dmbrubac]

246188828265473 | 10223*2^5796845+1
246188828265472 = 2^10*53*97*2111*22153

171388807977727 | 21181*2^5797244+1
171388807977726 = 2*3^2*83*139*6247*132113

437621215726002191369 | 4847*2^5803263+1 <-- the new 2nd largest factor of the year :|party|:
437621215726002191368=2^3*43*211*227*7127*19441*191693

2015485189907779 | 4847*2^5801991+1
2015485189907778=2*7*263*17921*3054449

5172107658035209 | 21181*2^5804804+1 <-- submitted about an hour before it would have gone to PRP :smoking:
5172107658035208=2^3*3*11*16193*19759*61231

[Nuri]

21143274634835342257 | 55459*2^5890846+1


21143274634835342256 = 2 ^ 4 x 3 x 23 x 31 x 3119 x 4021 x 4091 x 12041

[hc_grove]

It's been more than a week since the last one, but now I found:
16865935315528471 | 10223*2^5884637+1
284817113042325587201 | 55459*2^5874526+1
1927699125194094887 | 22699*2^5874598+1


16865935315528470 = 2*3*5*17*113*4483*5791*11273
(second one is larger than 2^64, I will factor that tomorrow).
1927699125194094886 = 2*653*709*1259*11467*144203

[Mystwalker]

Originally posted by hc_grove
284817113042325587201 | 55459*2^5874526+1

(second one is larger than 2^64, I will factor that tomorrow).

284 817113 042325 587200 = 2 ^ 8 x 5 ^ 2 x 37 x 43 x 89 x 547 x 2333 x 246277



And found one myself:
2918283220459681 | 55459*2^5868118+1

2918 283220 459680 = 2 ^ 5 x 3 x 5 x 29 x 509 x 6011 x 68521

[hc_grove]

Originally posted by Mystwalker
284 817113 042325 587200 = 2 ^ 8 x 5 ^ 2 x 37 x 43 x 89 x 547 x 2333 x 246277


Thanks. Now 2^8 that's something I haven't seen before.

[dmbrubac]

I had a 2^10 a few days back (see my previous post).

[Mystwalker]

8057451392817109 | 10223*2^5869769+1
8057 451392 817108 = 2 ^ 2 x 3 x 29 x 31 x 59 x 71 ^ 2 x 347 x 7237

[hc_grove]

3796805718943647229 | 24737*2^5951647+1

3796805718943647228 = 2^2*3^2*7*13*41*47*193*22751*136973

[hc_grove]

3025213428395171034079 | 28433*2^6051073+1

3025213428395171034078 = 2*3*43*83*353*367*599*7907*230239

[hc_grove]

3492869317679191 | 24737*2^6053911+1

3492869317679190 = 2*3*5*613*3251*3389*17239

[Frodo42]

Just found my first one with self-compiled factorer:

260840209049520371 | 21181*2^6103172+1

260840209049520370 = 2 x 5 x 179 x 367 x 1217 x 4363 x 74779
not very smooth (even though I don't really understand that term) but that counts in favor for the program.

[hc_grove]

65922812594639417 | 33661*2^6055008+1

65922812594639416 = 2^3*13^2*23*103*1483*1949*7121

[Frodo42]

oh boy oh boy oh boy

just found a big one
35935660269812747397727 | 4847*2^6168951+1

It's definetly the largest for 4847 so far, not all that smooth (or is it?)
35935 660269 812747 397726 = 2 x 3 ^ 2 x 19 x 29 x 367 x 2707 x 4651 x 5273 x 148711

[hc_grove]

It's been three weeks, but I finally found a new factor:
501737316342481 | 33661*2^6280416+1
501737316342480 = 2^4*3^4*5*19*47*317*273521

Apart from the last factor this is the smoothest I've seen.

[hc_grove]

Ahh, only two days.

5274028739098589 | 4847*2^6281463+1
5274028739098588 = 2^2*7*167*877*16993*75683

[Nuri]

235703760784331778069847 | 19249*2^6405242+1

235703760784331778069846 = 2 x 3 x 11 x 13 ^ 2 x 17 x 389 x 1427 x 2521 x 2791 x 318259

[Mystwalker]

Very smooth - apart from the last 'bummer'... :D

[Nuri]

6258055154249506859 | 4847*2^6508047+1

6258055154249506858 = 2 x 19 x 577 x 811 x 1151 x 14759 x 20717

[hc_grove]

622529950198081 | 55459*2^6821266+1

622529950198080 = 2^6*3*5*73*83*401*266897

Apart from the last factor this is extremely smooth.

But the main "feature" of this factor is that I used George's new factoring code to find it!

[Nuri]

11529059469964763 | 28433*2^6989137+1
11529059469964762 = 2 x 11 x 67 x 167 x 1787 x 4817 x 5441

10340964718983403 | 55459*2^6990238+1
10340964718983402 = 2 x 3 x 7 x 41 x 83 x 401 x 457 x 394811

1405455930948721 | 55459*2^6990250+1
1405455930948720 = 2 ^ 4 x 3 x 5 x 7 x 31 x 47 x 7793 x 73679

[Mystwalker]

524413893207156299 | 10223*2^6705785+1

524413893207156298 = 2 x 17 ^ 2 x 1091 x 1693 x 18287 x 26861

Would have been a B1 hit...

[hc_grove]

75249573592556119391 | 24737*2^6826063+1

75249573592556119390 = 2*5*43*557*1031*4111*4507*16447

Fairly smooth.

Would have been a stage 1 factor, but I used Georges new code.

[garo]

So does George's new code not do a GCD at the end of stage 1??

[Mystwalker]

Originally posted by garo
So does George's new code not do a GCD at the end of stage 1??

Depends on the setting of the ini file. I switched it off, as I think most factors will be found in the B2 stage...

[garo]

Well then it's a bit unfair to "blame" George's code for not finding it in stage 1. At least that's what hc_grove's post in particular and your post to some extent indicated.

[Mystwalker]

I'd rather say these postings were a bit misleading.
Of course, George's new algorithm would also find it with GCD after stage 1.

P.S.: If I can't blame George's code, I can blame himself for giving the tip to switch off stage 1 GCD. ;) :Pokes:

:spank: Ouch! Don't beat me again! Ouch! ;)

I hope you can forgive us. :cheers:

[hc_grove]

Sorry for causing confusion. I don't remember having turned off GCD at the end of stage 1, but if you say it's an option, that's probably right.

[hc_grove]

Notice the n of this factor:

204324288555810331 | 33661*2^6900000+1


204324288555810330 = 2*3^5*5*97*1543*6007*93523

[Frodo42]

Found in stage 1
14201216740129537 | 10223*2^6983885+1

14201216740129536 = 2 ^ 8 x 3 ^ 3 x 13 x 29 x 271 x 2671 x 7529

My smoothest factor yet :cheers:

[Frodo42]

P-1 found a factor in stage #2, B1=40000, B2=440000.
4847*2^7160703+1 has a factor: 1043098013353843

1043098013353842 = 2 x 3 ^ 5 x 5387 x 7127 x 55903

My first factor found with Geoges new code.
And I got my 9th place back, but not for all that long unless I find more factors.

[pixl97]

22699*2^7247638+1 has a factor: 581445854728607717657

This seems pretty large, am I wrong for thinking that?

581445854728607717656 = 2 ^ 3 x 17 ^ 2 x 37 x 2029 x 4643 x 11117 x 64901

[biwema]

Very smoth:

67607*2^9107451+1 has a factor: 4921636623093246299

4 921636 623093 246298 = 2 x 11 x 29 x 127 x 1553 x 2161 x 2531 x 7151

[vjs]

WoW,

That's great, but may I ask why you are factoring at such a high n-level?

There is nothing wrong with factoring a particular k and some n level, but please let us know that you have. I was personally thinking of doing some factoring around 13m to remove some of those ?33661? tests.

[biwema]

Sorry for not reserving, but I thought, that my range does not fit into the main range.

At the moment, I work on 67607 starting from 9million. Depending on how much time it takes I will continue until 9.3..10 million.

At the moment I use B1= 60000

Reason why I factor in that area:

No special reason. I like to play around with numbers.
I this case I want to bring the entry 67607 at 9..10M in MikeH's Database below 1000.
It's just for fun

:D

I will keep the factoring details, so you will have that information, when the main factoring effort reaches that area.

Reto

[vjs]

Thought you were trying to get an early start on the 200K point score :D...

As for your choice of B1, ... others will have to comment, sieving will probably reach 2^50 by then, but your goal is to reduce it to <1000 ...

I'd just worry about P-1'ing very lightly and having to redo them again later, otherwise I'd say knock yourself out.

I was considering doing the same sort of thing...

Trying to eliminate the k/n's in the range of 13460000 to 13470000 for those tests reported dropped http://www.seventeenorbust.com/secret.

I wish Alien88 would remove those 9999999 tests and place those 33661 tests back where they should be. :(

[biwema]

Originally posted by vjs
I'd just worry about P-1'ing very lightly and having to redo them again later, otherwise I'd say knock yourself out.


Do you think I should increase my bounds that it is not necessary to redo the work?

At the moment I am happy with the efficiency. I got 3 factors out of 100. unfortunately the biggest one disappeared.

P-1 found a factor in stage #2, B1=60000, B2=660000.
67607*2^9151371+1 has a factor: 17603629608134545337

I assume it is excluded because of a smaller factor of that number...

[MikeH]

unfortunately the biggest one disappeared. I just posted that factor into the large factor submission form (http://www.seventeenorbust.com/largesieve/) and it was accepted and added as new. I'd logged out, so all you need to do now is reserve the range in the factor forum and you'll get the credit. ;)

Largest factor of the year. :|party|:

EDIT: Just looked at the posts above, after noticing that all your last findings were 67607. Don't worry about reserving, I'll sort it on my side.

[vjs]

To me those bounds look good, perhaps someone with a second opinion...

I'd probably look more at the factor found per time then factors per number of tests. If you can get the same amount of factors in the same time with less tests that would be better of course. I think this can be done by increasing B1 and leaving B2 as is???

I'm not a factoring guy, but if I member correctly each time you factor a number a file will be created. You can use this file later to go back and choose different bounds and it takes less time etc...I wouldn't delete those files just yet.

We should be testing those numbers by mid to late year, so I don't think your efforts are in vien. Also when reservations get close or your finished with 9M-10M, you should make a post in the reservation section. Also if you get to 10M before main effort gets there you could always go back with different bounds if you keep those files...

[MikeH]

Largest factor of the year. :|party|: Make that second largest (http://www.aooq73.dsl.pipex.com/2005/ui/19999.htm) :blush:

[Mystwalker]

Originally posted by vjs
I'd probably look more at the factor found per time then factors per number of tests. If you can get the same amount of factors in the same time with less tests that would be better of course. I think this can be done by increasing B1 and leaving B2 as is???

The bounds are quite high (I'm not saying they are too high, though). Maybe factors/time is higher with lower bounds, but I don't know.
I wouldn't lower B1 only, as the optimal ratio between B1 and B2 is important for efficient factoring. As soon as 2 prime factors of the P-1 are > B1, the this factor won't be found by P-1. :(


I'm not a factoring guy, but if I member correctly each time you factor a number a file will be created. You can use this file later to go back and choose different bounds and it takes less time etc...I wouldn't delete those files just yet.

Those files can be re-used, right. But only under certain circumstances (which I can't remember) there won't be a lowered efficiency.

[biwema]

Interesting,

17603629608134545337 is less than 64 bits and should be submittable by the normal form. I thought it was accepted.

[vjs]

Your right, it should have been accepted with the <64-bit, everyone should remember to check their factor submissions regarless.

Since you are actually working quite a bit ahead of prp why don't you try slighly higher b1 b2 for 10 pairs for example. See how many more you get and what the increased time expenditure is.

I've tried factoring some smaller numbers with bounds as high as

b1=7000000
b2=17000000

I think this might be a little to large for those n>9m numbers... take ages etc.

If I had a fast p4 with alot of memory, I'd try b1=1000000 b2=5000000 just too see how long it would take and the chances etc.

If I understand correctly your chances of finding a factor with p-1 increase with n as well, it's the old time vs chance of factor. Since we are not at 9m yet you have the time to experiment.

[Nuri]

Originally posted by MikeH
EDIT: Just looked at the posts above, after noticing that all your last findings were 67607. Don't worry about reserving, I'll sort it on my side.

@ Biwema: Still, it might be a good idea to simply open a thread under factoring subforum to announce the work (ranges) you've done on 67607. That way, we can simply skip those 67607/n pairs that you've already tested. But, do this only if you're doing some massive work over there. I dunno, may be an n range of, say 1 million or more. :confused: If not, do not bother at all.

[vjs]

If I understand correctly he has started

k=67607 from 9M up and is currently around 9.3M

He is using bounds of

B1=60000, B2=660000

These bounds seem pretty reasonable... perhaps he shouldl clarify that he did start at 9M and is increasing systematically...

[Nuri]

Ooops, my bad. I should have read previous posts more carefully. :blush:

[vjs]

No problem Nuri,

I'm also really guessing that he has done all inbetween as well...

Can you comment on the bounds and possibilities of increasing those for better success.

His main goal is to reduce the 9M<n<10M for k=67607 to (prp tests < 1000)

sounds like just as good of a goal as any IMHO.

Also

17 603629 608134 545336 = 2 ^ 3 x 19 x 97 x 157 x 2473 x 18661 x 164789

So I guess B1=20000 B2=200000

Would have found this

[vjs]

Well looks like someone has already tried one of the large k/n and gave up in less than a week :( .

Just wondering if anyone has tried factoring any of these...

10223 13467677 (Now in dropped que :bang: lowest one )
24737 13467703 (looks like this one may be assigned but not dropped)
55459 13467718 (looks like this one may be assigned but not dropped)
24737 13467727 (Next to be assigned)
24737 13467751

[Keroberts1]

24737 13467703 (looks like this one may be assigned but not dropped)
I got this one will be done in a few hours actually

[vjs]

Wow!!!

How long did it take you to finish on what type of machine etc...

[Keroberts1]

about 27 days on a athalon xp 2400
running almost constantly butthere was some sieving going on too.

[Nuri]

1363473963746084778807 | 22699*2^8600311+1


I've aldo got this! 79.9T factor

79897555161219 | 22699*2^8600263+1


and this!!!! 70k factor (which was not verified buy te submission page, as one might expect)

70173 | 22699*2^8600217+1

[vjs]

Nuri sorry to say this but here are the factors that acutally exist between 8600215-8600265

k=27653 n=8600217
k=4847 n=8600223
k=4847 n=8600247
k=33661 n=8600256
k=24737 n=8600263

I think you may have a problem with your worktodo.ini

[Nuri]

Ooops!!! :blush:

I guess I know why..

[Nuri]

Corrected & restarted the range.. :)

[vjs]

It happens...

I had a question for the factoring guys...

How does one get the newest version on prime 95 to do stage1 only factoring with set b1 bounds of say 2M?

[Mystwalker]

Either assign too few memory to stage 2, or set the value for stage2 in the workfile to 1.

[vjs]

I'm not really even sure about the worktodo.ini values etc.

Perhaps we can make a stickpost with all of the factoring clients with links and examples of files to create and their contents.

I'm not sure what to write in the work to do ini

[Nuri]

Here's a sample...

Pfactor=21181,2,8601140,1,49,1.5
Pfactor=22699,2,8601238,1,49,1.5
Pfactor=19249,2,8601278,1,49,1.5
Pfactor=55459,2,8601286,1,49,1.5


or, did I get you wrong?

[vjs]

No, but thanks nuri this is a good example of the way a typical worktodo.ini should look...

But what if you only want to run first stage with a paricular B1.

Or potentially run P+1, not sure if prime95 will do this but the latest ECM program will. I just don't know how to add the switches etc.

[Nuri]

Hmmm. I found 645160797731449 | 4847*2^8799543+1 through P-1 and it was a bit disappointing to see it was already sieved...

May be it's time for me to move 49 (~563T) setting to something like 49.2 (~647T) to match with 98% sieve point..



Any suggestions?

Are you all using 49, or anyone using other cutoff point?

[Nuri]

And by the way, 49.3 seems very close to current 95% sieve point.

May be it's a good cut-off as well....

[hhh]

I'm using

Pfactor=xxxxx,2,8xxxxxx,1,49,1.6

with a Celeron 2.0 GHz, 110-170 MB assigned.
I find usually 1 factor per 100 tests (rough estimate). One test takes 2 hours and half.

With prime95, the cutoff doesn't support floating point numbers; 49.x isn't accepted. (Right?) And I don't think it is time to go to 50, as even like this, we are slower then the main effort. (Or should I try?)

What is the relation between memory need and the numbers? I don't have a lot and would like to use is as good as possible. Don't tell me to PRP -> registry.

[Frodo42]

Garo wrote and excellent explanation about these things.
hc_grove added the explanation to this page (http://www.sslug.dk/~grove/sbfactor/choosing_bounds.shtml)

[MikeH]

(from Feb 2004)
I was wrong, I just coded up a quick trialfactorer and it factors both your numbers and Louie's so fast the time command can't measure it (on my 2GHz laptop that does regular factoring in the background).

You can download a UNIX version of the program (called trial) and the source code (trial.c) here (http://www.sslug.dk/~grove/sbfactor/) (the same place as where you can get my version of the factorer).

You can give the program either p or p-1 as input it will figure that out.

It only works with numbers < 2^64.
hc_grove,

I don't see this program or the source on the linked page. If it's still available (in particular the source) I'd be very interested. Thanks.

[Joe O]

Originally posted by hhh
With prime95, the cutoff doesn't support floating point numbers; 49.x isn't accepted. (Right?)
The latest, and fastest version for most machines, is 24.6. And yes it does accept floating point numbers for the last two parameters.

[garo]

Frodo42, thanks for the plug ;)

The latest version of Prime95 DOES support floating point arguments so using 49.3 is not a problem.

P-1 does not do a complete check in the same way that sieving does. The P-1 limits are defined by B1 and B2. The 49 or 49.3 is just used to help determine the "optimal" B1 and B2 as I explained in the above mentioned post. Note that your factor -1 has these two largest factors: 2393 x 118343. So any limits where B1 was greater than 2393 and B2 was greater than 118343 would have found this factor.

It is unfortunate that you wasted your time on finding this factor but the solution is to filter out numbers that have already been factored and not change the P-1 limits (though that may be necessary for other reasons).

Bottomline: Sieving and P-1 find factors in different ways so messing with limits will not ensure NO overlap. P-1 should NOT be done on numbers that have alerady been factored.

[hc_grove]

Originally posted by MikeH
hc_grove,

I don't see this program or the source on the linked page. If it's still available (in particular the source) I'd be very interested. Thanks.

I don't remember if it's susposed to be available on the page, but here's the source.



/* Written by Henrik Christian Grove */
/* Released as beerware */

#include <stdlib.h>
#include <stdio.h>

int main(int argc, char *argv[])
{
unsigned long long number;
char *endptr[10];
unsigned long div = 2;
unsigned int exp = 0;

if (argc != 2) {
printf("Error!\n");
exit(-1);
}
number = strtoll(argv[1],endptr,10);
if ((number % 2) == 1) {
number--;
}
printf("Factoring %llu\n",number);

printf("%llu = ",number);
while ((number % 2) == 0) {
exp++;
number /= 2;
}
if (exp > 1) {
printf("2^%u*",exp);
} else {
printf("2*");
}

div = 3;
while (div < number) {
exp = 0;
while ((number % div) == 0) {
exp++;
number /= div;
}
switch (exp) {
case 0:
break;
case 1:
printf("%lu*",div);
break;
default:
printf("%lu^%u*",div,exp);
}
div +=2;
}
printf("%llu\n",number);

exit(0);
}

[Nuri]

Originally posted by garo
It is unfortunate that you wasted your time on finding this factor but the solution is to filter out numbers that have already been factored and not change the P-1 limits (though that may be necessary for other reasons).

Bottomline: Sieving and P-1 find factors in different ways so messing with limits will not ensure NO overlap. P-1 should NOT be done on numbers that have alerady been factored.

I of course filter out regularly, but to be honest, only befor I dump my worktodo.ini, so once every week or so.

645.161T 4847 8799543 6.452 Sat 26-Feb-2005 156112.697 (2) (http://www.aooq73.dsl.pipex.com/2005/ui/7192.htm)

There is only five days between engracio submitted his factor and the date I commented on bad luck on my side. So, you decide... ;)


Still, I do think it would be better to use decimals. This is simply because, it gives a better estimate on what to expect and the relative feasibility of doing factoring for that k/n pair.

[garo]

Well, I guess this was just sheer bad luck for you.

[hhh]

First, I just wanted to post these two because I think they are beautiful; simple coincidence, though, I guess.

2400062667363983| 33661*2^8786592+1 (2 109 10193 10429 103567)
2448491069125963| 4847*2^8786607+1 (2 3 3 7 6947 28807 97103)

And then I realized that I was logged out while submitting:rolleyes: ; It's because of my browser, I guess, if I log in, and put the sieve submission page in the command line, I'm logged out again, even with 'remember my computer'. I have to click me until there. Sorry so much... If you decide that it's too much work, I will not be angry either.:)
(But if you want to do it, it's hh, not hhh, the account name)
See you, H.

[hc_grove]

I finally have a factor that's really worth bragging about: :D

191074725996848743974112872853597 | 67607*2^9999491+1

If I'm not complete mistaken, this is the second largest factor for a n>10000 we've ever found, to make it a little bit funnier, I'm the one who found the largest one too (36 digits, this one only has 33). :neener: :jester: :|party|: :elephant:

:help: Unfortunately this number is to large for my trial factorer, and I don't have java here, so I can't use the online ECM factoring thing Louie has told about, so I'm neither able to factor this p (to see if it's prime) nor p-1 (to see how smooth it is). :Pokes:

I was using quite (approaching the absurd) large bounds (B1=135000, B2=1991250) to find this, but without knowing how smooth it is, I can't tell whether that actually made a difference or just was a waste of time.

[Nuri]

???

191 074725 996848 743974 112872 853596 = 2 ^ 2 x 3 ^ 2 x 7 x 758233 039670
034698 309971 717673

Number of divisors: 36

Sum of divisors: 551 993652 879785 260369 659410 466672

Euler's Totient: 54 592778 856242 498278 317963 672384

Moebius: 0

Sum of squares: a^2 + b^2 + c^2 + d^2
a = 11057 584279 459218
b = 7388 520780 436290
c = 3769 851063 803796
d = 50 393782 390434


Side note:

758233 039670 034698 309971 717673 is prime

Number of divisors: 2

Sum of divisors: 758233 039670 034698 309971 717674

Euler's Totient: 758233 039670 034698 309971 717672

Moebius: -1

Sum of squares: a^2 + b^2
a = 619 909546 902227
b = 611 510583 170488

[vjs]

Hold on a sec did you factor this using p-1???

Or P+1 or ecm

[prime95]

191074725996848743974112872853597 = 9750606540977083 * 19596188728757959

[hc_grove]

Originally posted by vjs
Hold on a sec did you factor this using p-1???


Yes.

[hc_grove]

Originally posted by prime95
191074725996848743974112872853597 = 9750606540977083 * 19596188728757959

And:
9750606540977082 = 2*3*11^2*139*112361*859933
19596188728757958 = 2*3*83*4159*8669*1091401

[wblipp]

Originally posted by hc_grove
I don't have java here, so I can't use the online ECM factoring thing.

Dario Alpern's factoring applet at http://www.alpertron.com.ar/ECM.HTM

says

9750606540977083 x 19596188728757959

[Frodo42]

just found myself a 24 digit factor ... my second largest factor so far

P-1 found a factor in stage #2, B1=40000, B2=440000.
55459*2^9155398+1 has a factor: 267877184000769088280263

P-1 factorized:
267877 184000 769088 280262 = 2 x 3 ^ 3 x 7 x 13 x 613 x 643 x 15199 x 27427 x 331769

[Nuri]

Originally posted by biwema
Sorry for not reserving, but I thought, that my range does not fit into the main range.

At the moment, I work on 67607 starting from 9million. Depending on how much time it takes I will continue until 9.3..10 million.

At the moment I use B1= 60000

Reason why I factor in that area:

No special reason. I like to play around with numbers.
I this case I want to bring the entry 67607 at 9..10M in MikeH's Database below 1000.
It's just for fun

:D

I will keep the factoring details, so you will have that information, when the main factoring effort reaches that area.

Reto

Does anyone know if biwema did go through all k/n pairs for k=67607 and 9m<n<10m?

There are two reasons I'm asking that.

First of all, if he did so, may be P-1 factorers might consider skipping k=67607 and 9m<n<10m pairs.

And secondly, I would like to see that particular statistic to have a number <1000, meaning 36 more factors to be found. ;) Just for the fun of course. But, to be honest, I dunno how much work it would require. If it would need to much work, may be I'll simply save it for later (i.e. at least a couple of months from now). It looks like, the figure will drop to 1000- before sieving reaches 2^52. Long way to go... So, any feedback would be appreciated.

[biwema]

Hi
Sorry for not answering for such a long time.
I was quite busy all the time.

Finally, I worked on 67607 until 9.3 million and stopped then. On one machine I changed to proth numbers, the other has a mainboard failure and is not running now. therefore I have to change the drive first, before I can tell the exact bounds, but I think it was B1 =60000 from 9.1 to 9.3

Regards,
Reto

[hc_grove]

Well, it seems that I have some special gift for finding really large factors, I just got this one:
5767642985639413495402269732331|28433*2^9985657+1

It's only 31 digits and thus only comes third among my factors in size, but it still 5 digits more than MikeH's largest, which is now number four on the list of large factors (for n>10000 - if we only consider n>100000, MikeH is still in fourth place but a digit further behind).

And I still don't have Java on this machine, so I can't use the online ECM factoring thing for factoring p (to see if it's prime) or p-1 (to see how smooth it is).

I think this calls for some
:music:, :corn: and :drink:
in short: :|party|: :|party|: :|party|:
:cheers:

[Frodo42]

Originally posted by hc_grove
Well, it seems that I have some special gift for finding really large factors, I just got this one:
5767642985639413495402269732331|28433*2^9985657+1

It's only 31 digits and thus only comes third among my factors in size, but it still 5 digits more than MikeH's largest, which is now number four on the list of large factors (for n>10000 - if we only consider n>100000, MikeH is still in fourth place but a digit further behind).

And I still don't have Java on this machine, so I can't use the online ECM factoring thing for factoring p (to see if it's prime) or p-1 (to see how smooth it is).


Congrats again ... you do have a certain nack for these factors.

As with the others this one is also not prime though ... the Alpatrons jave applet took some time to find this (1 minute 38 seconds), it came out with:

5 767642 985639 413495 402269 732331 = 1255 267090 431443 x 4594 753602 324617

[hc_grove]

Originally posted by Frodo42
5 767642 985639 413495 402269 732331 = 1255 267090 431443 x 4594 753602 324617

Thanks, it's quote far from being smooth:

1255267090431442 = 2*11*5779*10529*937721
4594753602324616 = 2^3*29*257*61511*1252819

[hc_grove]

Originally posted by hc_grove
Well, it seems that I have some special gift for finding really large factors, I just got this one:
5767642985639413495402269732331|28433*2^9985657+1


The sad part is, that we found a prime for k=28433 back in january :(
Seems I forgot to update the dat.

[vjs]

Which program are you using to find these factors second what type of bounds are you using?

Nice find and wow thats a huge factor!!!!

Your B1 bound must be quite large if it's p-1

[hc_grove]

Originally posted by vjs
Which program are you using to find these factors second what type of bounds are you using?

Nice find and wow thats a huge factor!!!!

Your B1 bound must be quite large if it's p-1

The first and largest factor (the one with 36 digits - found before Louie started this thread) was found with sbfactor using optimal bounds (sieve depth = <whatever was relevant at the time>, factor value = 1.5 and RAM=512 i think).

The two new was found with mprime using some parameters that are chosen for getting high bounds, and the values actually used is: B1=135000 and B2=1991250.
I'm perfectly aware that this is not optimal for the project, but I'm also in this for the fun, and I like finding the less smooth factors (which seems to increase the probablity of finding large factors too).

As the factor isn't prime, you should actually think of it as being two factors found simultaneously. To find both factors (and thus the product)
B1 only had to be >= 61511 and
B2 only had to be >= 1252819,
to find the smoother (which would have been enough to eliminate the test - if we didnøt already have a prime for k=28433) all that was needed was:
B1 >= 10529 and B2 >= 937721.

What's really clear is that my B1 is way larger than needed, while B2 is only a factor 2 larger than needed.

[vjs]

I was just curious, it was obvious using alpertron that it was the multiple of two fairly large smooth factors.

And I'm all for using large B1 B2 bounds wondering if you would really find that many more if you were using optimal bounds anyways.

[garo]

Read my writeup on hc_grove's site. He definitely would have found more factors in the same time with smaller bounds but he probably wouldn't have found factors as large.

[Greenbank]

3551338609857586 | 19249*2^9660686+1

p-1 = 2 * 31 * 71 * 421 * 8209 * 233437

Submitted on webpage however I'm still waiting to get my lost password issue sorted but I'd like to make sure I get credit for it (especially as it's in the upcoming window :-)

[Frodo42]

I am doing some fast factoring with pretty low bounds ... I sure didn't expect this one

P-1 found a factor in stage #1, B1=20000.
22699*2^9782902+1 has a factor: 23397089200776608159181803

23 397089 200776 608159 181802 = 2 x 107 x 109 x 313 x 2657 x 2713 x 4241 x 5591 x 18749

For a factor of 26 digits this seems to be very smooth.

[Greenbank]

1005612431486479611763 | 21181*2^9668132+1

Woohoo.

p-1 is 2 * 3 * 11 * 43 * 181 * 449 * 823 * 39829 * 133013

[hc_grove]

I just found a quite smooth factor over 2^64:

316782611247570464197 | 33661*2^9674568+1

316782611247570464196 = 2 ^ 2 x 3 ^ 4 x 79 x 607 x 1423 x 1787 x 2081 x 3853

[vjs]

Just curious what people are using for B1 B2 bounds lately.

Looking at the numbers in the threads, etc.

- There are a little less than 250 (~244) tests in a 10000 range
- People are getting about 4 factors per 10000.

This boils down to one factor every ~60 tests.

I'm assuming people are using the latest version of Prime95 with default settings???

[Greenbank]

I'm using sbfactor v1.25.5

With 1GB of mem on a 3.0GHz Xeon it does B1=40000 B2=430000

With 256MB of mem on a 1.7GHz P4 it uses B1=40000 B2=370000.

Should I be using something else?

[Frodo42]

I think that is the same bounds that I am using at the moment.

I am using mprime v. 24.13 and with the with 49.5,1.5 at the end of my lines in worktodo.ini I get the following bounds
B1=40000, B2=430000
on my P4 3 GHz with 512 MB ram available for factoring.

[vjs]

Greenbank,

I think sbfactor is slower than Prime95, you probably have a feeling already of how long it take to factor one test.

Give Prime95 a try and see how long it takes using that program.

Creating a worktodo.ini isn't as confusing as it initally looks when usings Mike's make program.

Check the link at the top of the page.

I personally prefer larger bounds but prime95 was written by people who really know what they are doing. So the defaults that frodo mentioned are probably best. Yours are pratically identical.

If we had a shortage of numbers I.E. we ranges were not being passed by etc I'd suggest larger bounds.

[Frodo42]

He this is efficient ... I wish the factors were always this dense ... two in a row ;)



[Thu Aug 11 18:04:31 2005]
P-1 found a factor in stage #2, B1=40000, B2=430000.
21181*2^9802124+1 has a factor: 17993672443299947
[Thu Aug 11 19:04:50 2005]
P-1 found a factor in stage #2, B1=40000, B2=430000.
19249*2^9802202+1 has a factor: 27491241436006571

[vjs]

We don't really have alot of people factoring...

If people have time perhaps they can post the factors that they found, and do the following.

Go to this site... http://www.alpertron.com.ar/ECM.HTM

Enter the factor in frodos case

27491241436006571 press factor --> proves that the factor is prime to begin with.

Then subtract 1 and factor it again see what the factors are

27491 241436 006570 = 2 x 5 x 499 x 1579 x 12197 x 286061

12197 would have been the minimum B1 required
286061 would have been the minimum B2 required

17993672443299947

17993 672443 299946 = 2 x 23 x 241 x 419 x 33749 x 114781

33749 would have been the minimum B1 required
114781 would have been the minimum B2 required

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

I know we use to do this in the past.

[vjs]

Example only three lines,

P-1 found a factor in stage #2, B1=40000, B2=430000.
19249*2^9802202+1 has a factor: 27491241436006571

27491 241436 006570 = 2 x 5 x 499 x 1579 x 12197 x 286061

Would be great.

[Greenbank]

(B1=40000 B2=370000)
1596714224499631 | 22699*2^9750934+1
p-1 = 2*3*3*5*31*37*1597*2647

[Greenbank]

(B1=40000,B2=370000)
112967067451648889 | 24737*2^9754231+1
p-1 = 2 * 2 * 2 * 19 * 19 * 97 * 179 * 181 * 1033 * 12049

[hc_grove]

3521346658647360362333 | 33661*2^9872640+1

3521346658647360362332 = 2 ^ 2 x 23 x 31 x 11003 x 18217 x 39839 x 154619

Found with optimal bounds for sieve depth = 49.7, factor value = 1.5, and RAM = 512 MB (B1=40000, B2=400000).

[Mystwalker]

That was really a very close hit. Congratz, hc_grove! :thumbs:

[hc_grove]

Just found this one:
18196089861334501 | 10223*2^10101065+1

18196089861334500 = 2^2*3^3*5^3*37*47*701*997*1109

Now, that's smooth! (But, I've seen even smoother)

[Greenbank]

Nice, and that was just above where my range stopped! Nothing on my first one with B1=600000,B2=1M. Bah.

The lowest B2 for a factor > 2^49 was found by sieving:-

512099950585939 (49 bits)

512099950585938 = 2 x 3 x 11^2 x 13^2 x 29 x 41 x 103 x 173 x 197

(B1 = 173, B2 = 197)

The lowest B1 for a factor > 2^49 was:-

582971265917041 (50 bits)

582971265917040 = 2^4 x 3 x 5 x 7 x 11 x 13 x 19 x 37 x 61 x 71 x 797

(B1 = 71, B2 = 797)

[vjs]

Woot!!!

Looks like that was me and engracio, respectively.

:D :cheers: :D

[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... :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. :smoking:

[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. :smoking:

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.:blush:

[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 :Pokes: 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. :smoking:

[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 :D

[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. :clap:

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.