Contribution and Reservation

(67·10¹⁹⁸+23)/9 =: 7(4)₁₉₇7_<199>; = 1061 · 1721 · 13309 · 7524529636303_<13> · 335978832747224663_<18> · 11137645550920823922623_<23> · [10879425119128136867510341310339065508484984737418999522353088128986982306666008217873556615079205565104225641789566254364931151683455169_<137>] SUBMIT/RESERVE

Status

Expression:	(67·10¹⁹⁸+23)/9
Composite Factor:	108794251191281368675103413103390655084849847374189995223530 881289869823066660082178735566150792055651042256417895662543 64931151683455169 (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 201.22-digit and the GNFS difficulty is 136.04-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 74447_198.
Put the following polynomial file 74447_198.poly in there too.
And then, run "perl factMsieve.pl 74447_198".

74447_198.poly ^*1

# Murphy_E = 4.096671e-11, selected by Jeff Gilchrist
n: 10879425119128136867510341310339065508484984737418999522353088128986982306666008217873556615079205565104225641789566254364931151683455169
Y0: -170457057417434125112276689
Y1: 1550362629278389
c0: -1072923066164245678352319539490336
c1: 35947841973863292864061107840
c2: -126210859678647736593714
c3: -6085750686352187
c4: 176404403478
c5: 75600
skew: 784057.89
type: gnfs
# selected mechanically
rlim: 14200000
alim: 14200000
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	500	Erik Branger	Jan 30, 2009
		1850	Wataru Sakai	Aug 31, 2009
		2350 / 2350
45	11e6	0 / 3961
45	11e6	/ 3961
50	43e6	0 / 7465 (1129)
50	43e6	/ 7465 (1129)
55	11e7	0 / 17751 (3097)
55	11e7	/ 17751 (3097)
60	26e7	0 / 42014 (7636)
60	26e7	/ 42014 (7636)

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

echo 10879425119128136867510341310339065508484984737418999522353088128986982306666008217873556615079205565104225641789566254364931151683455169 | ecm -n -c 3961 11e6

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

echo 10879425119128136867510341310339065508484984737418999522353088128986982306666008217873556615079205565104225641789566254364931151683455169 | ecm -n -c 7465 43e6

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

echo 10879425119128136867510341310339065508484984737418999522353088128986982306666008217873556615079205565104225641789566254364931151683455169 | ecm -n -c 17751 11e7

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

echo 10879425119128136867510341310339065508484984737418999522353088128986982306666008217873556615079205565104225641789566254364931151683455169 | 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