Contribution and Reservation

(38·10¹⁹⁸-11)/9 =: 4(2)₁₉₇1_<199>; = 3 · 47 · 1823 · 1110719 · 5483341 · 9631771 · 480069323 · 8335036117_<10> · 92991198633973667_<17> · [752534499961367908323419835432278965141241263613794849800559645888450395458093315354479300187884037333469548246405613740423618402927558339_<138>] SUBMIT/RESERVE

Status

Expression:	(38·10¹⁹⁸-11)/9
Composite Factor:	752534499961367908323419835432278965141241263613794849800559 645888450395458093315354479300187884037333469548246405613740 423618402927558339 (138-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 200.98-digit and the GNFS difficulty is 137.88-digit. GNFS must be faster than SNFS. It will take about 15 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 42221_198.
Put the following polynomial file 42221_198.poly in there too.
And then, run "perl factMsieve.pl 42221_198".

42221_198.poly ^*1

# Murphy_E = 2.602339e-11, selected by Jeff Gilchrist
n: 752534499961367908323419835432278965141241263613794849800559645888450395458093315354479300187884037333469548246405613740423618402927558339
Y0: -370603112381685254156146343
Y1: 2394773936983783
c0: 1601876436722378740324333136374020
c1: -11953380860331230609455872768
c2: -55428898699295519721773
c3: 284272152287479742
c4: 284392404312
c5: 107640
skew: 451451.19
type: gnfs
# selected mechanically
rlim: 16000000
alim: 16000000
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 138-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	500	Erik Branger	Apr 20, 2009
		1611	Wataru Sakai	Nov 25, 2009
		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 752534499961367908323419835432278965141241263613794849800559645888450395458093315354479300187884037333469548246405613740423618402927558339 | ecm -n -c 3974 11e6

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

echo 752534499961367908323419835432278965141241263613794849800559645888450395458093315354479300187884037333469548246405613740423618402927558339 | ecm -n -c 7469 43e6

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

echo 752534499961367908323419835432278965141241263613794849800559645888450395458093315354479300187884037333469548246405613740423618402927558339 | ecm -n -c 17752 11e7

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

echo 752534499961367908323419835432278965141241263613794849800559645888450395458093315354479300187884037333469548246405613740423618402927558339 | 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