Contribution and Reservation

(52·10¹⁸⁵-43)/9 =: 5(7)₁₈₄3_<186>; = 3² · 7 · 30000315797_<11> · 232490372587643_<15> · 174803429130286213921446816952979_<33> · [7522107521443271223466183633469728712100415963742065209003855874361356379684995803913837842415410103835151008458204515220434919_<127>] (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=3852562354 for P33 / Apr 2, 2009) SUBMIT/RESERVE

Status

Expression:	(52·10¹⁸⁵-43)/9
Composite Factor:	752210752144327122346618363346972871210041596374206520900385 587436135637968499580391383784241541010383515100845820451522 0434919 (127-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 186.72-digit and the GNFS difficulty is 126.88-digit. GNFS must be faster than SNFS. It will take about 5 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 57773_185.
Put the following polynomial file 57773_185.poly in there too.
And then, run "perl factMsieve.pl 57773_185".

57773_185.poly ^*1

# Murphy_E = 1.120012e-10, selected by Jeff Gilchrist
n: 7522107521443271223466183633469728712100415963742065209003855874361356379684995803913837842415410103835151008458204515220434919
Y0: -2983877102863315702915276
Y1: 73379265821081
c0: 45160442475153815242573586272827
c1: 886707757037453366496659031
c2: -2367591708403568239449
c3: -31638284319711139
c4: 23099476234
c5: 31800
skew: 366735.95
type: gnfs
# selected mechanically
rlim: 8100000
alim: 8100000
lpbr: 28
lpba: 28
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 127-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	Apr 3, 2009
35	1e6	118 / 0
40	3e6	500	Erik Branger	May 11, 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 7522107521443271223466183633469728712100415963742065209003855874361356379684995803913837842415410103835151008458204515220434919 | ecm -n -c 1818 3e6

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

echo 7522107521443271223466183633469728712100415963742065209003855874361356379684995803913837842415410103835151008458204515220434919 | ecm -n -c 4365 11e6

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

echo 7522107521443271223466183633469728712100415963742065209003855874361356379684995803913837842415410103835151008458204515220434919 | ecm -n -c 7534 43e6

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

echo 7522107521443271223466183633469728712100415963742065209003855874361356379684995803913837842415410103835151008458204515220434919 | 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