Contribution and Reservation

(35·10²⁰⁰+1)/9 =: 3(8)₁₉₉9_<201>; = 17² · 29 · 293 · 3999019603_<10> · 200892193437289_<15> · 6728470765532169399958286068096229_<34> · [29297402016470524234096481937774452825853317683256295975854623540072654392659095875611433521676001164170111844716196224386736672898007231_<137>] (Makoto Kamada / GMP-ECM 6.2.1 B1=25e4, sigma=1961032907 for P34 / Dec 5, 2008) SUBMIT/RESERVE

Status

Expression:	(35·10²⁰⁰+1)/9
Composite Factor:	292974020164705242340964819377744528258533176832562959758546 235400726543926590958756114335216760011641701118447161962243 86736672898007231 (137-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 201.54-digit and the GNFS difficulty is 136.47-digit. GNFS must be faster than SNFS. It will take about 13 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 38889_200.
Put the following polynomial file 38889_200.poly in there too.
And then, run "perl factMsieve.pl 38889_200".

38889_200.poly ^*1

# Murphy_E = 3.066763e-11, selected by Jeff Gilchrist
n: 29297402016470524234096481937774452825853317683256295975854623540072654392659095875611433521676001164170111844716196224386736672898007231
Y0: -200182175767581342975231256
Y1: 1603916686072249
c0: -844910762074244614331247539996745
c1: 4818106201142303185355875436
c2: 34943211072326182403955
c3: -50684125350902958
c4: -181772665528
c5: 91140
skew: 466419.18
type: gnfs
# selected mechanically
rlim: 14600000
alim: 14600000
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 137-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	2111	Wataru Sakai	Apr 5, 2009
40	3e6	2111 / 2111
45	11e6	0 / 3974
45	11e6	/ 3974
50	43e6	0 / 7469 (1133)
50	43e6	/ 7469 (1133)
55	11e7	0 / 17752 (3098)
55	11e7	/ 17752 (3098)
60	26e7	0 / 42014 (7636)
60	26e7	/ 42014 (7636)

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

echo 29297402016470524234096481937774452825853317683256295975854623540072654392659095875611433521676001164170111844716196224386736672898007231 | ecm -n -c 3974 11e6

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

echo 29297402016470524234096481937774452825853317683256295975854623540072654392659095875611433521676001164170111844716196224386736672898007231 | ecm -n -c 7469 43e6

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

echo 29297402016470524234096481937774452825853317683256295975854623540072654392659095875611433521676001164170111844716196224386736672898007231 | ecm -n -c 17752 11e7

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

echo 29297402016470524234096481937774452825853317683256295975854623540072654392659095875611433521676001164170111844716196224386736672898007231 | ecm -n -c 42014 26e7

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