ECM factoring

[rogue]

Originally Posted by michaf

Darn :)

When I posted I did just miss the list of composites...
which ones do you have left rogue?
And to what limits ecm'd?

oh, and I noticed P+1 factors in it; did you find those with ecmnet too?
(as in, do you use an automated process, or do you pick at them by hand? If automatic, where can I grab the process?)

yet another thing, can we have a list of the 100 smallest numbers with no factors reported for Riesel & Sierpinski?

Cheers, Micha

Yes, I used ECMNet to find all of these. I will have to get back to you on how far I went with ECM/P-1/P+1. You can d/l ECMNet from my homepage (you can find it via google or in the Factoring group). I can e-mail you the ecmserver.ini file if you want to go further.

[michaf]

Ah thanks :)
I'd love to have the remaining .ini;

I'm reading up on cygwin and how to compile the source now, if I can't handle it I reckon I'll be back for you to beg for binaries as well...

I still had a very ancient version 2.5, no P+1, P-1 whatsoever... it sounds like it has evolved quite a bit :)

[michaf]

Compiling is way easier then I ever thought it would be :)

[rogue]

Originally Posted by michaf

Ah thanks :)
I'd love to have the remaining .ini;

I'm reading up on cygwin and how to compile the source now, if I can't handle it I reckon I'll be back for you to beg for binaries as well...

I still had a very ancient version 2.5, no P+1, P-1 whatsoever... it sounds like it has evolved quite a bit :)

PM me your e-mail for the ini file. I've done some additional work (after discovering a couple of bugs).

[rogue]

Here are some new factors. I'm stopping ECM and will use msieve on some of the smaller values.

Factor=(190468*5^181-1)/8350696811068256679952273 Method=ECM B1=11000000 Sigma=1285010070
Factor=(181754*5^182-1)/2038698488746960115415779 Method=P+1 B1=11000000 Sigma=0
Factor=(266206*5^129-1)/30696985392105649 Method=P+1 B1=1000000 Sigma=0
Factor=(175124*5^186-1)/513588340906647766621082933 Method=ECM B1=1000000 Sigma=387918309
Factor=(190334*5^174-1)/823918283555893175077567 Method=P+1 B1=3000000 Sigma=0
Factor=(326962*5^139-1)/4186471592323524772673 Method=P+1 B1=1000000 Sigma=0

[rogue]

Here are some msieve results:

284422*5^111-1 = 24038835244148619355105310827970092056793 * 4557432513506183772340688157886113663859093

49568*5^112-1 = 16787766406466816943097 * 5686551335775831395789060458827887112528891832450138913812567

244564*5^111-1 = 10235335327328061980017 * 224857569528631275881429 * 40931100608358616777499432662719730343

304004*5^112-1 = 883084520450978709728220967157 * 663006080680131978154637822997889030237473302457773207

[rogue]

A few more msieve results:

189766*5^113-1 = 128813458021380247369861 * 14186251477152607987765725365428134521770770726991162393990009

183916*5^117-1 = 42399397852905162380996534754127 * 26106600977032862532541765126445390338869673510178192437

211208*5^114-1 = 973721884734396620927419741 * 8659468398229276068706514519953664908695299344206982378639

181754*5^118-1 = 525613102235449055987356891572797687 * 10405867857680251957451696478807929370674014157800127

[rogue]

Two more msieve results. It would be better to switch back to ECMNet for the others for a while.

171362*5^120-1 = 13205387043574681401291550997 * 9762564312563427551375397101214318209341244980682709191661917

./msieve 297016*5^121-1 = 1774080468990376518855677314795669 * 629762874830636929719348759785786852734923901938425592571

There are no more composites less than 90 digits.

[masser]

Just found and submitted these with some quick mprime P-1 runs....

7210637297104627 | 70082*5^128-1 
54664922438141 | 146756*5^176-1 
37076275916074565239 | 22966*5^199-1 
395101795983287 | 164852*5^204-1 
13915365963895553 | 227968*5^221-1 
78065486929245307 | 127174*5^231-1 
3664230465186135494231 | 95662*5^239-1 
5599383752622756663491 | 53542*5^271-1 
489654805514261194891 | 181754*5^278-1 
6354534201861413 | 301562*5^330-1 
190223578435224840641 | 53546*5^392-1 
507438630988444678349 | 151026*5^410-1 
86063612368176106063 | 146756*5^412-1 
131088948239432129497 | 98038*5^441-1 
6614589777190617023 | 131848*5^447-1 
574445557854580903 | 150344*5^516-1 
3374450414375580161 | 211208*5^540-1 
6676783195589983833332361409 | 263432*5^566-1 
5908875585165836527 | 304004*5^596-1 
2236864379520079 | 34354*5^639-1 
512375570213359 | 173198*5^644-1 
170119868528826049 | 64598*5^654-1 
11815154236447 | 4906*5^661-1 
3234648857970913 | 292648*5^673-1 
79597251147600827 | 35816*5^674-1 
28003933052519310841 | 3622*5^711-1 
415435099650058329623 | 101284*5^528+1
52467536732556811 | 10918*5^1332+1
829218408585403 | 109208*5^481+1
1740782526434467 | 110242*5^380+1
83008569135731 | 110488*5^1468+1
5386693058844337 | 110488*5^940+1
244115802429647 | 111382*5^1504+1
4210979187208951 | 111382*5^454+1
478943558034593 | 118568*5^469+1
765577640155986497381 | 118568*5^741+1
105139662064361 | 123748*5^1120+1
2895344320339 | 123748*5^1292+1
15008610360923 | 127312*5^1140+1
20288985899446773857 | 127312*5^1404+1
1588352442499 | 138514*5^1230+1
1433187238796590953925091 | 152588*5^771+1
6505622632049 | 154222*5^1182+1
921913997699843 | 154222*5^1348+1
1149941877019357 | 177742*5^649-1
1174156561050195731 | 200062*5^257-1
121664461662516457957154127262589496751 | 200062*5^293-1
2543201155069541 | 207394*5^205-1
85234125089152788851 | 243944*5^508-1

[jasonp]

Originally Posted by masser

7210637297104627 | 70082*5^128-1

I didn't see the complete factorization of this number in previous posts, so...

$ msieve -v "(70082*5^128-1)/7210637297104627"
factoring 2856231415474432974944212479854659271054467580145259335332537697794
127608187 (79 digits)

prp20 factor: 95005088536679698589
prp59 factor: 30063983513595644103640396803691356370355990204630108417783

Incidentally, Intel dual-core machines *suck* at running msieve. A 1GHz athlon is almost as fast as a 3GHz Pentium D, and I've received reports that more recent Intel dual-core machines aren't much better. It may just be bad tuning, but it may also be high cache latency.

jasonp

[tnerual]

all the P4 family (p4, pentium D) suck at sieving.

the core 2 duo family is much better

in fact everything is good at sieving except the P4 and pentium D