Contribution and Reservation

10²²¹-9 =: (9)₂₂₀1_<221>; = 2244243292414987_<16> · [44558448871375226540373951962642129976734728458907558245705265151925208084969966648536859456690150287256166432931650825893163912246227886931197577078948493557862621208139168368158344454752222607848944122693_<206>] SUBMIT/RESERVE

Status

Expression:	10²²¹-9
Composite Factor:	445584488713752265403739519626421299767347284589075582457052 651519252080849699666485368594566901502872561664329316508258 931639122462278869311975770789484935578626212081391683681583 44454752222607848944122693 (206-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.

SNFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 221.70-digit and the GNFS difficulty is 205.65-digit. SNFS must be faster than GNFS. It will take about 102 CPU-days to factor this composite number on 64-bit Opteron-2600MHz.

Put factMsieve.pl to which $GGNFS_BIN_PATH and $NUM_CPUS were modified properly in the working directory 99991_221.
Put the following polynomial file 99991_221.poly in there too.
And then, run "perl factMsieve.pl 99991_221".

99991_221.poly ^*1

n: 44558448871375226540373951962642129976734728458907558245705265151925208084969966648536859456690150287256166432931650825893163912246227886931197577078948493557862621208139168368158344454752222607848944122693
m: 5000000000000000000000000000000000000
deg: 6
c6: 32
c0: -45
skew: 1.06
type: snfs
lss: 1
rlim: 35000000
alim: 35000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6

*1 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 206-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	0 / 0
45	11e6	600	Dmitry Domanov	May 11, 2009
		719	Dmitry Domanov	Jun 30, 2009
		1319 / 4479
		/ 3160
50	43e6	0 / 7257 (901)
50	43e6	/ 7257 (901)
55	11e7	0 / 17687 (3011)
55	11e7	/ 17687 (3011)
60	26e7	0 / 41997 (7608)
60	26e7	/ 41997 (7608)

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

echo 44558448871375226540373951962642129976734728458907558245705265151925208084969966648536859456690150287256166432931650825893163912246227886931197577078948493557862621208139168368158344454752222607848944122693 | ecm -n -c 3160 11e6

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

echo 44558448871375226540373951962642129976734728458907558245705265151925208084969966648536859456690150287256166432931650825893163912246227886931197577078948493557862621208139168368158344454752222607848944122693 | ecm -n -c 7257 43e6

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

echo 44558448871375226540373951962642129976734728458907558245705265151925208084969966648536859456690150287256166432931650825893163912246227886931197577078948493557862621208139168368158344454752222607848944122693 | ecm -n -c 17687 11e7

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

echo 44558448871375226540373951962642129976734728458907558245705265151925208084969966648536859456690150287256166432931650825893163912246227886931197577078948493557862621208139168368158344454752222607848944122693 | ecm -n -c 41997 26e7

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