Contribution and Reservation

10¹⁹⁶+9 =: 1(0)₁₉₅9_<197>; = 409 · 24509 · 24568382659368173_<17> · 44401499461295046411183451748843306897700065477_<47> · [914485651586525533357484598772878668557145673386605657821723195587345693907083602731033750236232276619318600012074196323998309_<126>] (Wataru Sakai / GMP-ECM 6.1 B1=11000000, sigma=2570867251 for P47 / Nov 11, 2006) SUBMIT/RESERVE

Status

Expression:	10¹⁹⁶+9
Composite Factor:	914485651586525533357484598772878668557145673386605657821723 195587345693907083602731033750236232276619318600012074196323 998309 (126-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 196.00-digit and the GNFS difficulty is 125.96-digit. GNFS must be faster than SNFS. It will take about 4 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 10009_196.
Put the following polynomial file 10009_196.poly in there too.
And then, run "perl factMsieve.pl 10009_196".

10009_196.poly ^*1

# Murphy_E = 1.351230e-10, selected by Jeff Gilchrist
n: 914485651586525533357484598772878668557145673386605657821723195587345693907083602731033750236232276619318600012074196323998309
Y0: -2144555406043205821893227
Y1: 61024673734267
c0: -818182740052913052462095914974900
c1: 1380025804792599906456170268
c2: 3878402356972635969483
c3: -12185887410032392
c4: 21368068
c5: 20160
skew: 646983.34
type: gnfs
# selected mechanically
rlim: 7600000
alim: 7600000
lpbr: 27
lpba: 27
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5

*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 126-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	0 / 956
40	3e6	/ 956
45	11e6	400	Serge Batalov	Jan 16, 2009
		400 / 4479 (677)
		/ 4079 (277)
50	43e6	0 / 7464 (1163)
50	43e6	/ 7464 (1163)
55	11e7	0 / 17744 (3096)
55	11e7	/ 17744 (3096)

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

echo 914485651586525533357484598772878668557145673386605657821723195587345693907083602731033750236232276619318600012074196323998309 | ecm -n -c 956 3e6

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

echo 914485651586525533357484598772878668557145673386605657821723195587345693907083602731033750236232276619318600012074196323998309 | ecm -n -c 4079 11e6

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

echo 914485651586525533357484598772878668557145673386605657821723195587345693907083602731033750236232276619318600012074196323998309 | ecm -n -c 7464 43e6

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

echo 914485651586525533357484598772878668557145673386605657821723195587345693907083602731033750236232276619318600012074196323998309 | ecm -n -c 17744 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