Contribution and Reservation

10²²²+3 =: 1(0)₂₂₁3_<223>; = 643 · [1555209953343701399688958009331259720062208398133748055987558320373250388802488335925349922239502332814930015552099533437013996889580093312597200622083981337480559875583203732503888024883359253499222395023328149300155521_<220>] SUBMIT/RESERVE

Status

Expression:	10²²²+3
Composite Factor:	155520995334370139968895800933125972006220839813374805598755 832037325038880248833592534992223950233281493001555209953343 701399688958009331259720062208398133748055987558320373250388 8024883359253499222395023328149300155521 (220-digit)
Status:	Not factored. Not reserved. You can submit its factors or reserve it for submitting in the future.

How to factor it

ECM, P-1, P+1

Look for prime factors by GMP-ECM first. Refer to the section "Efforts by ECM". Not only ECM but also P-1/P+1 may be helpful.

NFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 222.00-digit and the GNFS difficulty is 219.19-digit. SNFS must be faster than GNFS. It will take about 105 CPU-days to factor this composite number on 64-bit Opteron-2600MHz.

Steps of SNFS

Put factMsieve.pl to which $GGNFS_BIN_PATH and $NUM_CPUS were modified properly in the working directory 10003_222.
Put the following polynomial file 10003_222.poly in there too.
And then, run "perl factMsieve.pl 10003_222".

10003_222.poly

n: 1555209953343701399688958009331259720062208398133748055987558320373250388802488335925349922239502332814930015552099533437013996889580093312597200622083981337480559875583203732503888024883359253499222395023328149300155521
m: 10000000000000000000000000000000000000
deg: 6
c6: 1
c0: 3
skew: 1.20
type: snfs
lss: 1
rlim: 35000000
alim: 35000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6

These parameters were not fully adjusted. The approximate expressions which were used for making the parameters are: deg=expt<=105?4:expt<=210?5:6 or expt<=144?4:6; d=log10(c[deg])+deg*log10(m)[digits]; time=10^(d/30-4)[hours]; skew=|c0/c[deg]|^(1/deg); rlim=round(7*10^(d/60+3)); lpbr=floor(d/25+21); mfbr=floor(d/8+31); rlambda=floor(d/25+18)/10;

Efforts by ECM

The efforts by ECM to find small factors of this 220-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 40-digit or more. Please report your efforts by ECM. (Anonymous reports are not acceptable)

Level	B1	Reported runs Total / Required runs (Required runs for lower level)	Name
40	3e6	260	Serge Batalov	Dec 16, 2008
40	3e6	260 / 0
45	11e6	20	Serge Batalov	Dec 16, 2008
		400	Serge Batalov	Jan 17, 2009
		800	Dmitry Domanov	Jan 11, 2010
		1220 / 4421
		/ 3201
50	43e6	0 / 7270 (913)
50	43e6	/ 7270 (913)
55	11e7	0 / 17691 (3016)
55	11e7	/ 17691 (3016)
60	26e7	0 / 41998 (7610)
60	26e7	/ 41998 (7610)

Command line to find prime factors up to about 45-digit

echo 1555209953343701399688958009331259720062208398133748055987558320373250388802488335925349922239502332814930015552099533437013996889580093312597200622083981337480559875583203732503888024883359253499222395023328149300155521 | ecm -n -c 3201 11e6

Command line to find prime factors up to about 50-digit

echo 1555209953343701399688958009331259720062208398133748055987558320373250388802488335925349922239502332814930015552099533437013996889580093312597200622083981337480559875583203732503888024883359253499222395023328149300155521 | ecm -n -c 7270 43e6

Command line to find prime factors up to about 55-digit

echo 1555209953343701399688958009331259720062208398133748055987558320373250388802488335925349922239502332814930015552099533437013996889580093312597200622083981337480559875583203732503888024883359253499222395023328149300155521 | ecm -n -c 17691 11e7

Command line to find prime factors up to about 60-digit

echo 1555209953343701399688958009331259720062208398133748055987558320373250388802488335925349922239502332814930015552099533437013996889580093312597200622083981337480559875583203732503888024883359253499222395023328149300155521 | ecm -n -c 41998 26e7

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