Gratuitous factors thread - Page 40

Yeong Uk Jo · 2017-12-18, 12:18

62 digits factor with B1=11M

Quote:

GMP-ECM 6.4.4 [configured with GMP 6.0.0, --enable-asm-redc] [ECM]
Input number is 82947977904152216142981487498180726186239574056614106448293710350093705739494787849857984466404173813703400332132192914293468146933172793131 (140 digits)
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=8522999498
Step 1 took 24788ms
Step 2 took 8561ms
********** Factor found in step 2: 70414360667590677359732409234954190690337846850783209447865413
Found probable prime factor of 62 digits: 70414360667590677359732409234954190690337846850783209447865413
Probable prime cofactor 1177998026506691471724678243331372598110798297236722504137680826899502036749487 has 79 digits

Dubslow · 2017-12-18, 12:22

Wow, that's a pretty incredible find right there. Nice going

AndrewWalker · 2017-12-18, 12:40

Quote:

Originally Posted by sean

My total curves on 139!+1 are 6285 at B1=850M (including those I previously reported). I'll stop work on this number now.

Sean Irvine? I was working on factorial numbers +-1 well over 10 years ago and had a web page on them but haven't looked at them for a very long time. I remember you sent me lots of factors! Mainly searching for amicable pairs since then! Where are results kept nowdays, is Paul Leyland still working on these?

Andrew

sean · 2017-12-18, 20:19

Quote:

Originally Posted by AndrewWalker

Sean Irvine? I was working on factorial numbers +-1 well over 10 years ago and had a web page on them but haven't looked at them for a very long time. I remember you sent me lots of factors! Mainly searching for amicable pairs since then! Where are results kept nowdays, is Paul Leyland still working on these?

Andrew

Yes, it is the same me. There is no longer a website devoted to the factorial numbers -- in fact the ECMNET page still attempts to link to your old non-existent page. I have files with all the results I know about with dates and who found them. These days most results can be found in http://http://factordb.com/index.php, but there is no attribution or date information included there.

You're likely to be somewhat underwhelmed by the progress in the last 10 years. I think back then there were a few outstanding in the n=100 to 110 range, we've moved as far as the 130s. Some of the more recent factorizations have been completed by Womack, others at NFS@Home, and myself.

Paul (xilman) is active in this community, but I don't think he works or maintains up to date lists on these numbers.

Here's what I have as current status:

Code:

Smallest composites:
  -: 167!-1 C181, 145!-1 C185, 176!-1 C205, 136!-1 C214, 179!-1 C220
  +: 169!+1 C193, 139!+1 C202, 165!+1 C202, 172!+1 C205, 150!+1 C213
First holes:
  -: 136!-1 C214, 139!-1 C222, 141!-1 C235, 142!-1 C232, 145!-1 C185
  +: 139!+1 C202, 140!+1 C242, 146!+1 C223, 148!+1 C239, 150!+1 C213

fivemack · 2018-01-07, 15:00

139!+1 is sieving now, about 1% progress on the sieving per day so I expect to have some factors by the middle of Spring.

lorgix · 2018-02-10, 12:56

This was moderately surprising;

Code:

GMP-ECM 7.0.4-dev [configured with GMP 6.1.1, --enable-asm-redc] [ECM]
Input number is (3761^197-1)/((3761-1)) (701 digits)
Using B1=4561, B2=5900000, polynomial x^1, sigma=2:5488031021996423492
Step 1 took 234ms
Step 2 took 531ms
********** Factor found in step 2: 562895925799601989596986963845579
Found prime factor of 33 digits: 562895925799601989596986963845579
Composite cofactor ((3761^197-1)/((3761-1)))/562895925799601989596986963845579 has 669 digits

Dubslow · 2018-02-18, 11:27

Just saw this nice aliquot GNFS split, where the factors are within a factor-of-5 of each other

Code:

P53 = 14217452470664756386193874192650652909587358452024711
P53 = 68258578113070612746045366396559681840264538845755689

unconnected · 2018-03-16, 22:26

From 355950:i3100:

Code:

GMP-ECM 6.4.3 [configured with GMP 5.0.5, --enable-asm-redc] [ECM]
Input number is 411957627119775385989446575095474922185011137757112191784280518543958234873694230248024231153654496440498346403470812602522290113950341 (135 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=559213464
Step 1 took 3503ms
Step 2 took 2204ms
********** Factor found in step 2: 10569114423707394666840460729453391212643716992655339366569371941409
Found composite factor of 68 digits: 10569114423707394666840460729453391212643716992655339366569371941409
Probable prime cofactor 38977497130291302211279801679050238712241241117209766296388154315749 has 68 digits

C68 splits as P32*P36.

Alfred · 2018-04-29, 08:15

Code:

c279 = (10^279-31)/3
p126 = 683879988020855531843693974570809301443699094596561661475690616530795260027595121999433189270322605879651156172622984209245483
p153 = 487414954629682825615832070972614806528916687946252096353904135012248024359341728973161931019907828745530880376748837466333831896764672674769452527632481

unconnected · 2018-04-29, 14:36

Alfred, congratulations for two new records for near-repdigit project - for largest snfs factorization and biggest factor!

What hardware were used for sieving and LA and how many cpu-days are spent?

Alfred · 2018-04-29, 20:16

Thank you.

My hardware was a 32-core Xeon E5 v2 @ 3.4 GHz and a mix with the equivalent of 64 cores @ 2.8 GHz.

Collecting ~520e6 unique relations took about 520e6 sec (taking into account the duplicates), ~ 6000 cpu-days, This is a roughly estimation, not an accurate measuring.

LA was done with the real existing 32-core Xeon and took nearly 500hrs.
timestamps in the log-file do not reflect my breaks in the LA phase.

2018-02-18, 11:27	#436
Dubslow Basketry That Evening! "Bunslow the Bold" Jun 2011 40<A<43 -89<O<-88 3·29·83 Posts	Just saw this nice aliquot GNFS split, where the factors are within a factor-of-5 of each other Code: P53 = 14217452470664756386193874192650652909587358452024711 P53 = 68258578113070612746045366396559681840264538845755689

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2017-12-18, 12:22	#431
Dubslow Basketry That Evening! "Bunslow the Bold" Jun 2011 40<A<43 -89<O<-88 3·29·83 Posts	Wow, that's a pretty incredible find right there. Nice going

2018-01-07, 15:00	#434
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 2³×11×73 Posts	139!+1 is sieving now, about 1% progress on the sieving per day so I expect to have some factors by the middle of Spring.

2018-04-29, 14:36	#439
unconnected May 2009 Russia, Moscow 2,593 Posts	Alfred, congratulations for two new records for near-repdigit project - for largest snfs factorization and biggest factor! What hardware were used for sieving and LA and how many cpu-days are spent?

2018-04-29, 20:16	#440
Alfred May 2013 Germany 5×17 Posts	Thank you. My hardware was a 32-core Xeon E5 v2 @ 3.4 GHz and a mix with the equivalent of 64 cores @ 2.8 GHz. Collecting ~520e6 unique relations took about 520e6 sec (taking into account the duplicates), ~ 6000 cpu-days, This is a roughly estimation, not an accurate measuring. LA was done with the real existing 32-core Xeon and took nearly 500hrs. timestamps in the log-file do not reflect my breaks in the LA phase.