Contribution and Reservation

(2·10²⁰⁰-11)/9 =: (2)₁₉₉1_<200>; = 3 · 7 · 14001880603763633983098127_<26> · 249790641645802510176227421442280099_<36> · [302555921974370475370998169294219199252084902441380482697802372630541007145563557322381282854361483076742218761588448860732153113329663037_<138>] (Makoto Kamada / GMP-ECM 5.0.3 B1=79550, sigma=3513416514 for P26) (JMB / GMP-ECM B1=1000000, sigma=4272223135 for P36 / Aug 6, 2007) SUBMIT/RESERVE

Status

Expression:	(2·10²⁰⁰-11)/9
Composite Factor:	302555921974370475370998169294219199252084902441380482697802 372630541007145563557322381282854361483076742218761588448860 732153113329663037 (138-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 200.30-digit and the GNFS difficulty is 137.48-digit. GNFS must be faster than SNFS. It will take about 15 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 22221_200.
Put the following polynomial file 22221_200.poly in there too.
And then, run "perl factMsieve.pl 22221_200".

22221_200.poly ^*1

# Murphy_E = 2.780115e-11, selected by Jeff Gilchrist
n: 302555921974370475370998169294219199252084902441380482697802372630541007145563557322381282854361483076742218761588448860732153113329663037
Y0: -314532222429653569306286607
Y1: 2312616486368731
c0: 588210334255612666282036767029417600
c1: 1000989268530164537039272693640
c2: -1367472622085510555043846
c3: -582664283411125385
c4: 455283763786
c5: 98280
skew: 1779320.16
type: gnfs
# selected mechanically
rlim: 15600000
alim: 15600000
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 138-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	500	Erik Branger	Mar 21, 2009
		1727	Wataru Sakai	Apr 20, 2009
		2227 / 2227
45	11e6	0 / 3968
45	11e6	/ 3968
50	43e6	0 / 7467 (1131)
50	43e6	/ 7467 (1131)
55	11e7	0 / 17751 (3098)
55	11e7	/ 17751 (3098)
60	26e7	0 / 42014 (7636)
60	26e7	/ 42014 (7636)

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

echo 302555921974370475370998169294219199252084902441380482697802372630541007145563557322381282854361483076742218761588448860732153113329663037 | ecm -n -c 3968 11e6

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

echo 302555921974370475370998169294219199252084902441380482697802372630541007145563557322381282854361483076742218761588448860732153113329663037 | ecm -n -c 7467 43e6

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

echo 302555921974370475370998169294219199252084902441380482697802372630541007145563557322381282854361483076742218761588448860732153113329663037 | ecm -n -c 17751 11e7

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

echo 302555921974370475370998169294219199252084902441380482697802372630541007145563557322381282854361483076742218761588448860732153113329663037 | 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