Contribution and Reservation

7·10¹⁹³-9 =: 6(9)₁₉₂1_<194>; = 148773167 · 490799597 · 624265043 · 279332624936131460064588188231867_<33> · [5497668581305396532401907450640749152944535033751322787659919739277511451694105836805483559749328381395643428084855176167494056065079389_<136>] (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=3695353944 for P33 / Dec 24, 2007) SUBMIT/RESERVE

Status

Expression:	7·10¹⁹³-9
Composite Factor:	549766858130539653240190745064074915294453503375132278765991 973927751145169410583680548355974932838139564342808485517616 7494056065079389 (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 195.24-digit and the GNFS difficulty is 135.74-digit. GNFS may 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 69991_193.
Put the following polynomial file 69991_193.poly in there too.
And then, run "perl factMsieve.pl 69991_193".

69991_193.poly ^*1

# Murphy_E = 3.762873e-11, selected by Jeff Gilchrist
n: 5497668581305396532401907450640749152944535033751322787659919739277511451694105836805483559749328381395643428084855176167494056065079389
Y0: -143382507865235483658834141
Y1: 1403552824880639
c0: 658931677328103568891642171358336
c1: 14012452996056272554733098216
c2: 59480907608319418450354
c3: -116527973767666669
c4: -114106733592
c5: 90720
skew: 567017.3
type: gnfs
# selected mechanically
rlim: 14000000
alim: 14000000
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 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	Jo Yeong Uk	Feb 1, 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 5497668581305396532401907450640749152944535033751322787659919739277511451694105836805483559749328381395643428084855176167494056065079389 | ecm -n -c 3974 11e6

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

echo 5497668581305396532401907450640749152944535033751322787659919739277511451694105836805483559749328381395643428084855176167494056065079389 | ecm -n -c 7469 43e6

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

echo 5497668581305396532401907450640749152944535033751322787659919739277511451694105836805483559749328381395643428084855176167494056065079389 | ecm -n -c 17752 11e7

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

echo 5497668581305396532401907450640749152944535033751322787659919739277511451694105836805483559749328381395643428084855176167494056065079389 | 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