Contribution and Reservation

10²¹¹-9 =: (9)₂₁₀1_<211>; = 6277 · 23515656707_<11> · [67747107863082587477105411424345224422609764780486975662919251562496210922051419090545191361372504591023718788106923394075955127723744255135025064125333852948168854328720952394254817713278429554969_<197>] SUBMIT/RESERVE

Status

Expression:	10²¹¹-9
Composite Factor:	677471078630825874771054114243452244226097647804869756629192 515624962109220514190905451913613725045910237187881069233940 759551277237442551350250641253338529481688543287209523942548 17713278429554969 (197-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 211.00-digit and the GNFS difficulty is 196.83-digit. SNFS must be faster than GNFS. It will take about 45 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_211.
Put the following polynomial file 99991_211.poly in there too.
And then, run "perl factMsieve.pl 99991_211".

99991_211.poly ^*1

n: 67747107863082587477105411424345224422609764780486975662919251562496210922051419090545191361372504591023718788106923394075955127723744255135025064125333852948168854328720952394254817713278429554969
m: 100000000000000000000000000000000000
deg: 6
c6: 10
c0: -9
skew: 0.98
type: snfs
lss: 1
rlim: 23000000
alim: 23000000
lpbr: 29
lpba: 29
mfbr: 57
mfba: 57
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 197-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	703	Dmitry Domanov	Jun 30, 2009
		703 / 4479
		/ 3776
50	43e6	0 / 7396 (1077)
50	43e6	/ 7396 (1077)
55	11e7	0 / 17725 (3068)
55	11e7	/ 17725 (3068)
60	26e7	0 / 42006 (7625)
60	26e7	/ 42006 (7625)

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

echo 67747107863082587477105411424345224422609764780486975662919251562496210922051419090545191361372504591023718788106923394075955127723744255135025064125333852948168854328720952394254817713278429554969 | ecm -n -c 3776 11e6

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

echo 67747107863082587477105411424345224422609764780486975662919251562496210922051419090545191361372504591023718788106923394075955127723744255135025064125333852948168854328720952394254817713278429554969 | ecm -n -c 7396 43e6

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

echo 67747107863082587477105411424345224422609764780486975662919251562496210922051419090545191361372504591023718788106923394075955127723744255135025064125333852948168854328720952394254817713278429554969 | ecm -n -c 17725 11e7

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

echo 67747107863082587477105411424345224422609764780486975662919251562496210922051419090545191361372504591023718788106923394075955127723744255135025064125333852948168854328720952394254817713278429554969 | ecm -n -c 42006 26e7

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