ECM factoring

michaf · 2006-10-15, 08:48

Is there a way I can obtain a list of composites with n=110, which have no small factors, and have been found composite?

(For purpose of some ecm

ltd · 2006-10-15, 09:20

If i understand you request correct there is only one pair that suits your request:

151026*5^110-1

is the only one with n=110 where no factor is registered yet.

The composite is so small that i would not put to much effort into
ECM. After testing for around 20Digits i would switch to msieve.

Lars

michaf · 2006-10-15, 10:34

That was indeed what I meant.

If that is the only one, can you provide me with a list of the same criteria, but with n=105 to n=115
(assuming there will be around 10 candidates then :> )

Thanks in advance

Mystwalker · 2006-10-15, 15:26

Just entered 151026*5^110-1 into msieve:

prp41 factor: 19094485960440215874363137033854288407797
prp42 factor: 609318305575000443064617648157915891177117

So a relatively hard composite for ECM.

Lars:
If you want, you can provide a list of the smallest composites without factors (maybe up to 100 digits).

michaf · 2006-10-15, 16:19

Does anyone have a binary for Windows XP available of msieve;
I can't seem to connect to the website :(

Mystwalker · 2006-10-15, 16:54

I've uploaded it to http://www.mystwalker.de/msieve.exe

axn · 2006-10-15, 17:31

A list of numbers with n <= 200 (about 140-ish digits). Knock yourselves out

Code:

93254*5^111+1
71098*5^112+1
99784*5^112+1
139394*5^113+1
27676*5^114+1
45652*5^114+1
101284*5^120+1
110846*5^121+1
102482*5^123+1
67748*5^127+1
152588*5^129+1
60394*5^132+1
127312*5^132+1
93254*5^135+1
68492*5^137+1
76724*5^137+1
139606*5^138+1
93484*5^140+1
59912*5^141+1
36412*5^142+1
7528*5^144+1
110242*5^152+1
27676*5^154+1
33448*5^154+1
37328*5^155+1
83936*5^157+1
110846*5^157+1
67612*5^158+1
29914*5^164+1
45748*5^164+1
90056*5^167+1
37292*5^169+1
99926*5^169+1
37714*5^172+1
93484*5^172+1
99926*5^173+1
51208*5^176+1
71098*5^176+1
44348*5^179+1
60722*5^179+1
123748*5^180+1
24032*5^181+1
126134*5^181+1
32122*5^182+1
81556*5^184+1
45748*5^192+1
71098*5^196+1
45652*5^198+1
58642*5^198+1
44348*5^199+1

Code:

177742*5^111-1
244564*5^111-1
270694*5^111-1
284422*5^111-1
285598*5^111-1
49568*5^112-1
304004*5^112-1
189766*5^113-1
175124*5^114-1
211208*5^114-1
335414*5^114-1
22966*5^115-1
53542*5^115-1
326962*5^115-1
268514*5^116-1
183916*5^117-1
145484*5^118-1
181754*5^118-1
182398*5^119-1
193084*5^119-1
162668*5^120-1
171362*5^120-1
280558*5^121-1
297016*5^121-1
330286*5^123-1
66916*5^125-1
119878*5^125-1
287626*5^125-1
95662*5^127-1
159388*5^127-1
270694*5^127-1
284422*5^127-1
70082*5^128-1
289184*5^128-1
266206*5^129-1
170446*5^131-1
178658*5^132-1
248546*5^132-1
268168*5^133-1
331882*5^133-1
263432*5^134-1
52922*5^136-1
119878*5^137-1
136804*5^137-1
171748*5^137-1
105782*5^138-1
326962*5^139-1
250216*5^141-1
145484*5^142-1
45742*5^143-1
48394*5^143-1
57406*5^143-1
84466*5^145-1
156694*5^145-1
105782*5^146-1
326834*5^146-1
341552*5^146-1
49568*5^148-1
151026*5^149-1
227968*5^149-1
282316*5^151-1
151026*5^152-1
265702*5^155-1
82952*5^156-1
58882*5^157-1
151026*5^158-1
326834*5^158-1
177742*5^159-1
325846*5^159-1
23906*5^160-1
318278*5^160-1
1396*5^161-1
4906*5^161-1
254*5^162-1
301562*5^162-1
322498*5^163-1
76322*5^164-1
177742*5^165-1
47126*5^166-1
193084*5^167-1
329584*5^167-1
90082*5^169-1
305716*5^171-1
52922*5^172-1
146756*5^172-1
4906*5^173-1
201778*5^173-1
267298*5^173-1
114986*5^174-1
190334*5^174-1
146756*5^176-1
239342*5^176-1
119098*5^181-1
190468*5^181-1
181754*5^182-1
270694*5^183-1
291364*5^183-1
313126*5^183-1
330286*5^183-1
52922*5^184-1
254*5^186-1
22934*5^186-1
175124*5^186-1
195872*5^186-1
298442*5^186-1
22966*5^187-1
63838*5^187-1
170386*5^187-1
244564*5^187-1
270694*5^187-1
45742*5^191-1
244474*5^191-1
178658*5^192-1
146264*5^194-1
154844*5^194-1
181754*5^194-1
49568*5^196-1
162668*5^196-1
289184*5^196-1
155056*5^197-1
22966*5^199-1
326962*5^199-1
53546*5^200-1
109862*5^200-1
151026*5^200-1

michaf · 2006-10-15, 17:33

Thank you very much; works like a breeze :)

rogue · 2006-10-15, 23:02

Here are a few factors found with ECMNet:

Code:

  Factor=(114986*5^174-1)/379902756659932314540226757  Method=ECM  B1=50000  Sigma=317724188
  Factor=(145484*5^118-1)/70720022828927  Method=P+1  B1=11000  Sigma=0
  Factor=(146756*5^176-1)/54664922438141  Method=ECM  B1=4000  Sigma=3919738122
  Factor=(159388*5^127-1)/207744844379353  Method=ECM  B1=4000  Sigma=1808995376
  Factor=(162668*5^196-1)/433875207094892411  Method=ECM  B1=11000  Sigma=2582877610
  Factor=(178658*5^132-1)/8982269123892058877  Method=ECM  B1=4000  Sigma=762976299
  Factor=(178658*5^192-1)/175924146197165790157  Method=ECM  B1=4000  Sigma=1578730843
  Factor=(22966*5^115-1)/6145137373110220361  Method=ECM  B1=11000  Sigma=2502255553
  Factor=(244474*5^191-1)/12604574046969647  Method=ECM  B1=4000  Sigma=1938855787
  Factor=(270694*5^111-1)/9282654955784874686237  Method=ECM  B1=50000  Sigma=4266460859
  Factor=(284422*5^127-1)/306924591435787012637  Method=ECM  B1=11000  Sigma=1582262282
  Factor=(32122*5^182+1)/130638651980492717  Method=ECM  B1=11000  Sigma=4266957462
  Factor=(326962*5^115-1)/1020925597568325778191539  Method=P+1  B1=250000  Sigma=0
  Factor=(330286*5^123-1)/158471259457076034563  Method=ECM  B1=11000  Sigma=524053560
  Factor=(37292*5^169+1)/13842322175522083193  Method=ECM  B1=11000  Sigma=1644641442
  Factor=(44348*5^199+1)/16955700689371753  Method=ECM  B1=4000  Sigma=2698378633
  Factor=(45652*5^198+1)/2688181171747004147  Method=ECM  B1=11000  Sigma=2562229817
  Factor=(4906*5^161-1)/634601858622185420614757  Method=ECM  B1=50000  Sigma=4286256100
  Factor=(4906*5^173-1)/92427297981294512736881  Method=ECM  B1=50000  Sigma=21193133
  Factor=(52922*5^184-1)/93301874885777516011  Method=ECM  B1=11000  Sigma=933155666
  Factor=(53542*5^115-1)/458418141797417  Method=ECM  B1=4000  Sigma=3636869478
  Factor=(58642*5^198+1)/330921465926153  Method=ECM  B1=4000  Sigma=2089995963
  Factor=(70082*5^128-1)/7210637297104627  Method=P+1  B1=11000  Sigma=0
  Factor=(82952*5^156-1)/102056906295636737  Method=ECM  B1=11000  Sigma=3487385275
  Factor=(84466*5^145-1)/70564051565150093  Method=ECM  B1=11000  Sigma=3035267008
  Factor=(93484*5^140+1)/3169025325620488069  Method=ECM  B1=11000  Sigma=4229484020
  Factor=(110242*5^152+1)/20425567696228201219  Method=ECM  B1=11000  Sigma=3704238344
  Factor=(110846*5^157+1)/36894600680914771  Method=ECM  B1=11000  Sigma=3818262179
  Factor=(156694*5^145-1)/327006191082653  Method=ECM  B1=4000  Sigma=3577478552
  Factor=(162668*5^120-1)/85256087348126738693363423  Method=P-1  B1=1000000  Sigma=0
  Factor=(170386*5^187-1)/69698390156631852757  Method=ECM  B1=50000  Sigma=2836256888
  Factor=(170446*5^131-1)/17248118797340549  Method=P+1  B1=50000  Sigma=0
  Factor=(177742*5^111-1)/8195343775507391  Method=ECM  B1=4000  Sigma=2218838184
  Factor=(177742*5^159-1)/16063038136782011  Method=ECM  B1=11000  Sigma=3312015359
  Factor=(182398*5^119-1)/47173547661287921  Method=P+1  B1=11000  Sigma=0
  Factor=(193084*5^119-1)/3019144474204511  Method=ECM  B1=4000  Sigma=45234912
  Factor=(193084*5^167-1)/1429649390984524573  Method=ECM  B1=11000  Sigma=1425380224
  Factor=(22934*5^186-1)/172160876759587631695076377  Method=ECM  B1=250000  Sigma=1617428312
  Factor=(22966*5^199-1)/29100478681586969  Method=ECM  B1=4000  Sigma=1191682622
  Factor=(254*5^162-1)/9739118161967427559960039873  Method=ECM  B1=50000  Sigma=2879001303
  Factor=(266206*5^129-1)/30696985392105649  Method=ECM  B1=11000  Sigma=3666464973
  Factor=(267298*5^173-1)/34227798584171  Method=ECM  B1=4000  Sigma=4107368742
  Factor=(268514*5^116-1)/370068380371036213  Method=ECM  B1=11000  Sigma=1524499785
  Factor=(270694*5^183-1)/1101705109993493  Method=ECM  B1=4000  Sigma=2102509712
  Factor=(270694*5^187-1)/38463742897711  Method=P-1  B1=11000  Sigma=0
  Factor=(280558*5^121-1)/414576995606023390211  Method=ECM  B1=11000  Sigma=469015256
  Factor=(285598*5^111-1)/375749537040391  Method=ECM  B1=4000  Sigma=3157466552
  Factor=(291364*5^183-1)/1509357189919666267  Method=ECM  B1=11000  Sigma=2244193588
  Factor=(318278*5^160-1)/533790183710437  Method=P+1  B1=11000  Sigma=0
  Factor=(326834*5^158-1)/17246730850466681  Method=ECM  B1=11000  Sigma=3022016363
  Factor=(331882*5^133-1)/16984086107920411643  Method=ECM  B1=11000  Sigma=1661523515
  Factor=(33448*5^154+1)/1583005222600247  Method=ECM  B1=11000  Sigma=1692147828
  Factor=(335414*5^114-1)/5041036922451253  Method=ECM  B1=4000  Sigma=2725960821
  Factor=(37328*5^155+1)/4943409161782783229  Method=ECM  B1=4000  Sigma=179112494
  Factor=(45748*5^164+1)/470297374399093  Method=ECM  B1=4000  Sigma=515481127
  Factor=(57406*5^143-1)/375175202823019  Method=ECM  B1=4000  Sigma=2808855047
  Factor=(63838*5^187-1)/512447326408133276035429  Method=ECM  B1=50000  Sigma=2993800935
  Factor=(67612*5^158+1)/480360427198259852989  Method=ECM  B1=11000  Sigma=686894238
  Factor=(68492*5^137+1)/3686282618915677861429  Method=ECM  B1=50000  Sigma=1382748929
  Factor=(71098*5^196+1)/946115591700317747  Method=ECM  B1=11000  Sigma=3763056919
  Factor=(83936*5^157+1)/2112075140337902743  Method=ECM  B1=4000  Sigma=2429035105
  Factor=(95662*5^127-1)/531867303082334337347101  Method=ECM  B1=50000  Sigma=1838912073

rogue · 2006-10-16, 11:22

And a few more (I'm stopping for now):

Factor=(93484*5^172+1)/60782079140483440871979455131 Method=ECM B1=250000 Sigma=28191491
Factor=(29914*5^164+1)/63794339552597 Method=P-1 B1=50000 Sigma=0
Factor=(330286*5^183-1)/4958452917960746500313 Method=P+1 B1=3000000 Sigma=0
Factor=(76322*5^164-1)/5992764482366367690119 Method=ECM B1=11000 Sigma=1390406135
Factor=(105782*5^146-1)/133850862174409490091959 Method=P+1 B1=3000000 Sigma=0
Factor=(145484*5^142-1)/1937540863409699263307 Method=ECM B1=11000 Sigma=635604225
Factor=(244564*5^187-1)/3626922080959283609031329 Method=ECM B1=50000 Sigma=482724853
Factor=(109862*5^200-1)/28537924427147656121963 Method=P+1 B1=11000000 Sigma=0
Factor=(171362*5^120-1)/13205387043574681401291550997 Method=P+1 B1=11000000 Sigma=0
Factor=(326962*5^139-1)/4186471592323524772673 Method=P+1 B1=1000000 Sigma=0

michaf · 2006-10-16, 13:10

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

2006-10-15, 08:48	#1
michaf Jan 2005 479 Posts	ECM factoring Is there a way I can obtain a list of composites with n=110, which have no small factors, and have been found composite? (For purpose of some ecm

2006-10-16, 13:10	#11
michaf Jan 2005 1DF₁₆ Posts	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 Last fiddled with by michaf on 2006-10-16 at 13:15

2006-10-15, 09:20	#2
ltd Apr 2003 1100000100₂ Posts	If i understand you request correct there is only one pair that suits your request: 151026*5^110-1 is the only one with n=110 where no factor is registered yet. The composite is so small that i would not put to much effort into ECM. After testing for around 20Digits i would switch to msieve. Lars

2006-10-15, 10:34	#3
michaf Jan 2005 737₈ Posts	That was indeed what I meant. If that is the only one, can you provide me with a list of the same criteria, but with n=105 to n=115 (assuming there will be around 10 candidates then :> ) Thanks in advance

2006-10-15, 15:26	#4
Mystwalker Jul 2004 Potsdam, Germany 3·277 Posts	Just entered 151026*5^110-1 into msieve: prp41 factor: 19094485960440215874363137033854288407797 prp42 factor: 609318305575000443064617648157915891177117 So a relatively hard composite for ECM. Lars: If you want, you can provide a list of the smallest composites without factors (maybe up to 100 digits).

2006-10-15, 16:19	#5
michaf Jan 2005 479 Posts	Does anyone have a binary for Windows XP available of msieve; I can't seem to connect to the website :(

2006-10-15, 16:54	#6
Mystwalker Jul 2004 Potsdam, Germany 3·277 Posts	I've uploaded it to http://www.mystwalker.de/msieve.exe

2006-10-15, 17:33	#8
michaf Jan 2005 479 Posts	Thank you very much; works like a breeze :)

2006-10-16, 11:22	#10
rogue "Mark" Apr 2003 Between here and the 2²×7×223 Posts	And a few more (I'm stopping for now): Factor=(934845^172+1)/60782079140483440871979455131 Method=ECM B1=250000 Sigma=28191491 Factor=(299145^164+1)/63794339552597 Method=P-1 B1=50000 Sigma=0 Factor=(3302865^183-1)/4958452917960746500313 Method=P+1 B1=3000000 Sigma=0 Factor=(763225^164-1)/5992764482366367690119 Method=ECM B1=11000 Sigma=1390406135 Factor=(1057825^146-1)/133850862174409490091959 Method=P+1 B1=3000000 Sigma=0 Factor=(1454845^142-1)/1937540863409699263307 Method=ECM B1=11000 Sigma=635604225 Factor=(2445645^187-1)/3626922080959283609031329 Method=ECM B1=50000 Sigma=482724853 Factor=(1098625^200-1)/28537924427147656121963 Method=P+1 B1=11000000 Sigma=0 Factor=(1713625^120-1)/13205387043574681401291550997 Method=P+1 B1=11000000 Sigma=0 Factor=(3269625^139-1)/4186471592323524772673 Method=P+1 B1=1000000 Sigma=0