Contribution and Reservation

10¹⁹⁸+9 =: 1(0)₁₉₇9_<199>; = 225961 · 124678768297051697_<18> · 9690036302476528221435163969533038158217_<40> · [3663098565111345395412929971728350097530716199796536338138921821753864966157300030614431362264492489238686784881314038315456171995557481_<136>] (Wataru Sakai / GMP-ECM 6.1 B1=11000000, sigma=250750163 for P40 / Nov 15, 2006) SUBMIT/RESERVE

Status

Expression:	10¹⁹⁸+9
Composite Factor:	366309856511134539541292997172835009753071619979653633813892 182175386496615730003061443136226449248923868678488131403831 5456171995557481 (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.

NFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 198.00-digit and the GNFS difficulty is 135.56-digit. GNFS must be faster than SNFS. It will take about 13 CPU-days to factor this composite number on 64-bit Opteron-2600MHz.

Steps of GNFS

Put factMsieve.pl to which $GGNFS_BIN_PATH and $NUM_CPUS were modified properly in the working directory 10009_198.
Put the following polynomial file 10009_198.poly in there too.
And then, run "perl factMsieve.pl 10009_198".

10009_198.poly

# Murphy_E = 3.645535e-11, selected by Jeff Gilchrist
n: 3663098565111345395412929971728350097530716199796536338138921821753864966157300030614431362264492489238686784881314038315456171995557481
Y0: -131956436291492157976982759
Y1: 1296424507828307
c0: -4251511697945230867544865967400448
c1: 37679214937572173345550605176
c2: 124585683684350039775258
c3: -173847889987010841
c4: -216090152330
c5: 91560
skew: 760516.56
type: gnfs
# selected mechanically
rlim: 13800000
alim: 13800000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.6
alambda: 2.6

These parameters were not fully adjusted. The approximate expressions which were used for making the parameters are: d=log10(n); time=5*10^(d/20-5)[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 45-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
45	11e6	400	Serge Batalov	Jan 16, 2009
		4000	Wataru Sakai	Dec 12, 2009
		4400 / 4215
50	43e6	0 / 6521
50	43e6	/ 6521
55	11e7	0 / 17485 (2705)
55	11e7	/ 17485 (2705)
60	26e7	0 / 41946 (7521)
60	26e7	/ 41946 (7521)
65	85e7	0 / 69397 (13588)
65	85e7	/ 69397 (13588)

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

echo 3663098565111345395412929971728350097530716199796536338138921821753864966157300030614431362264492489238686784881314038315456171995557481 | ecm -n -c 6521 43e6

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

echo 3663098565111345395412929971728350097530716199796536338138921821753864966157300030614431362264492489238686784881314038315456171995557481 | ecm -n -c 17485 11e7

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

echo 3663098565111345395412929971728350097530716199796536338138921821753864966157300030614431362264492489238686784881314038315456171995557481 | ecm -n -c 41946 26e7

Command line to find prime factors up to about 65-digit

echo 3663098565111345395412929971728350097530716199796536338138921821753864966157300030614431362264492489238686784881314038315456171995557481 | ecm -n -c 69397 85e7

Contribution and Reservation

Status

How to factor it

ECM, P-1, P+1

NFS

Steps of GNFS

See also

Efforts by ECM

Submit polynomial for GNFS

Submit factors

Make reservation