Contribution and Reservation

(10¹⁹³+71)/9 =: (1)₁₉₂9_<193>; = 3 · 83 · 1431244686853_<13> · 4508363445277_<13> · 1413521664942116360011121415991_<31> · [489241024496907354315699990163522497568807868639472158427158410636880445374402685926600142762794996201973895068523081010022271307068961_<135>] (Wataru Sakai / GMP-ECM B1=10000000, sigma=3841290381 for P31) SUBMIT/RESERVE

Status

Expression:	(10¹⁹³+71)/9
Composite Factor:	489241024496907354315699990163522497568807868639472158427158 410636880445374402685926600142762794996201973895068523081010 022271307068961 (135-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 193.60-digit and the GNFS difficulty is 134.69-digit. GNFS may be faster than SNFS. It will take about 11 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 11119_193.
Put the following polynomial file 11119_193.poly in there too.
And then, run "perl factMsieve.pl 11119_193".

11119_193.poly ^*1

# Murphy_E = 4.407351e-11, selected by Jeff Gilchrist
n: 489241024496907354315699990163522497568807868639472158427158410636880445374402685926600142762794996201973895068523081010022271307068961
Y0: -95032253217668712025973218
Y1: 952981437474071
c0: -1583870051330964911784359128634595
c1: 9630335309103699344367650911
c2: -4804157391762369532926
c3: -54248772405774990
c4: 10785404612
c5: 63120
skew: 644731.19
type: gnfs
# selected mechanically
rlim: 13100000
alim: 13100000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
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 135-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	500	Erik Branger	Jan 31, 2009
		500 / 2350
		/ 1850
45	11e6	0 / 4370 (537)
45	11e6	/ 4370 (537)
50	43e6	0 / 7535 (1246)
50	43e6	/ 7535 (1246)
55	11e7	0 / 17766 (3126)
55	11e7	/ 17766 (3126)

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

echo 489241024496907354315699990163522497568807868639472158427158410636880445374402685926600142762794996201973895068523081010022271307068961 | ecm -n -c 1850 3e6

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

echo 489241024496907354315699990163522497568807868639472158427158410636880445374402685926600142762794996201973895068523081010022271307068961 | ecm -n -c 4370 11e6

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

echo 489241024496907354315699990163522497568807868639472158427158410636880445374402685926600142762794996201973895068523081010022271307068961 | ecm -n -c 7535 43e6

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

echo 489241024496907354315699990163522497568807868639472158427158410636880445374402685926600142762794996201973895068523081010022271307068961 | ecm -n -c 17766 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