Contribution and Reservation

(41·10²⁰¹-23)/9 =: 4(5)₂₀₀3_<202>; = 61 · 263 · 556399173320324616098443890467_<30> · 252635123955001705694176323303097_<33> · [2020112505647632756928351550824281446496761217400100731640375421833487154531131232240765574391378366318710959461855840758615958423877129_<136>] (Makoto Kamada / GMP-ECM 6.2.1 B1=25e4, sigma=1360197331 for P30 / Jan 28, 2009) (Makoto Kamada / GMP-ECM 6.2.1 B1=25e4, sigma=1337979874 for P33 / Jan 28, 2009) SUBMIT/RESERVE

Status

Expression:	(41·10²⁰¹-23)/9
Composite Factor:	202011250564763275692835155082428144649676121740010073164037 542183348715453113123224076557439137836631871095946185584075 8615958423877129 (136-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.

GNFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 202.61-digit and the GNFS difficulty is 135.31-digit. GNFS must be faster than SNFS. It will take about 12 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 45553_201.
Put the following polynomial file 45553_201.poly in there too.
And then, run "perl factMsieve.pl 45553_201".

45553_201.poly ^*1

# Murphy_E = 3.341096e-11, selected by Jeff Gilchrist
n: 2020112505647632756928351550824281446496761217400100731640375421833487154531131232240765574391378366318710959461855840758615958423877129
Y0: -122132585150291904233707681
Y1: 1136096084137561
c0: -25963798040440918980248684089558440
c1: 125639942954371025936724098526
c2: 11108069105080236956201
c3: -398834278669675529
c4: -87377149969
c5: 74340
skew: 1012849.33
type: gnfs
# selected mechanically
rlim: 13600000
alim: 13600000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.6
alambda: 2.6

*1 These parameters were not fully adjusted. The approximate expressions which were used for making the parameters are: d=log10(n); time=10^(d/21-4)[hours]; rlim=round(3*10^(d/37+3)); lpbr=floor(d/18+21); mfbr=floor(d/5+28); rlambda=floor(d/26+21)/10;

Efforts by ECM

The efforts by ECM to find small factors of this 136-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 35-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
35	1e6	0 / 0
40	3e6	400	Erik Branger	May 10, 2009
		400 / 2336
		/ 1936
45	11e6	0 / 4390 (561)
45	11e6	/ 4390 (561)
50	43e6	0 / 7538 (1252)
50	43e6	/ 7538 (1252)
55	11e7	0 / 17766 (3127)
55	11e7	/ 17766 (3127)

Command line to find prime factors up to about 40-digit

echo 2020112505647632756928351550824281446496761217400100731640375421833487154531131232240765574391378366318710959461855840758615958423877129 | ecm -n -c 1936 3e6

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

echo 2020112505647632756928351550824281446496761217400100731640375421833487154531131232240765574391378366318710959461855840758615958423877129 | ecm -n -c 4390 11e6

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

echo 2020112505647632756928351550824281446496761217400100731640375421833487154531131232240765574391378366318710959461855840758615958423877129 | ecm -n -c 7538 43e6

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

echo 2020112505647632756928351550824281446496761217400100731640375421833487154531131232240765574391378366318710959461855840758615958423877129 | ecm -n -c 17766 11e7

Contribution and Reservation

Status

How to factor it

ECM, P-1, P+1

GNFS

See also

Efforts by ECM

Submit polynomial for GNFS

Submit factors

Make reservation