Contribution and Reservation

(17·10¹⁹⁹+7)/3 =: 5(6)₁₉₈9_<200>; = 853 · 49108949 · 4690843055178469916009_<22> · 139439575860152525764642907000219_<33> · [2068145264829021522693134837565772375255413534314070907056190048608030188897413343095857160841289014207680735432647902934113992020248887_<136>] (Serge Batalov / GMP-ECM 6.2.2 B1=3000000, sigma=1353002088 for P33 / Mar 30, 2009) SUBMIT/RESERVE

Status

Expression:	(17·10¹⁹⁹+7)/3
Composite Factor:	206814526482902152269313483756577237525541353431407090705619 004860803018889741334309585716084128901420768073543264790293 4113992020248887 (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 201.23-digit and the GNFS difficulty is 135.32-digit. GNFS must 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 56669_199.
Put the following polynomial file 56669_199.poly in there too.
And then, run "perl factMsieve.pl 56669_199".

56669_199.poly ^*1

# Murphy_E = 3.602487e-11, selected by Jeff Gilchrist
n: 2068145264829021522693134837565772375255413534314070907056190048608030188897413343095857160841289014207680735432647902934113992020248887
Y0: -126837336283256420197649941
Y1: 1136632980239273
c0: -2274555397861336846611164246629200
c1: -62996330537901347005792952316
c2: 365200992979385926122968
c3: -55470358164208047
c4: 79748731590
c5: 63000
skew: 984079.87
type: gnfs
# selected mechanically
rlim: 13600000
alim: 13600000
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 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	118	Makoto Kamada	Mar 29, 2009
35	1e6	118 / 0
40	3e6	500	Erik Branger	May 9, 2009
		500 / 2318
		/ 1818
45	11e6	0 / 4365 (527)
45	11e6	/ 4365 (527)
50	43e6	0 / 7534 (1244)
50	43e6	/ 7534 (1244)
55	11e7	0 / 17765 (3125)
55	11e7	/ 17765 (3125)

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

echo 2068145264829021522693134837565772375255413534314070907056190048608030188897413343095857160841289014207680735432647902934113992020248887 | ecm -n -c 1818 3e6

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

echo 2068145264829021522693134837565772375255413534314070907056190048608030188897413343095857160841289014207680735432647902934113992020248887 | ecm -n -c 4365 11e6

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

echo 2068145264829021522693134837565772375255413534314070907056190048608030188897413343095857160841289014207680735432647902934113992020248887 | ecm -n -c 7534 43e6

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

echo 2068145264829021522693134837565772375255413534314070907056190048608030188897413343095857160841289014207680735432647902934113992020248887 | ecm -n -c 17765 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