Contribution and Reservation

(17·10¹⁹³-71)/9 =: 1(8)₁₉₂1_<194>; = 11 · 239 · 42509 · 2743602737_<10> · 92013106361783_<14> · 1226618192728483238346292651289_<31> · [545826498093011871441688642479259504041283061123554586469819861859389894946467489199080893852931993824875963703801740289530014752159_<132>] (Makoto Kamada / GMP-ECM 5.0.3 B1=78210, sigma=3973126487 for P31) SUBMIT/RESERVE

Status

Expression:	(17·10¹⁹³-71)/9
Composite Factor:	545826498093011871441688642479259504041283061123554586469819 861859389894946467489199080893852931993824875963703801740289 530014752159 (132-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 195.63-digit and the GNFS difficulty is 131.74-digit. GNFS must be faster than SNFS. It will take about 8 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 18881_193.
Put the following polynomial file 18881_193.poly in there too.
And then, run "perl factMsieve.pl 18881_193".

18881_193.poly ^*1

# Murphy_E = 6.567464e-11, selected by Jeff Gilchrist
n: 545826498093011871441688642479259504041283061123554586469819861859389894946467489199080893852931993824875963703801740289530014752159
Y0: -26192035923945107482766694
Y1: 354289823658071
c0: -4161857348336243365095111889625
c1: -36131836220448483862445345
c2: 851923949960810820509
c3: -1968275742107407
c4: 5386193268
c5: 44280
skew: 199837.02
type: gnfs
# selected mechanically
rlim: 10900000
alim: 10900000
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 132-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	Feb 3, 2009
		1850	Wataru Sakai	Nov 24, 2009
		2350 / 2350
45	11e6	0 / 3961
45	11e6	/ 3961
50	43e6	0 / 7465 (1129)
50	43e6	/ 7465 (1129)
55	11e7	0 / 17751 (3097)
55	11e7	/ 17751 (3097)
60	26e7	0 / 42014 (7636)
60	26e7	/ 42014 (7636)

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

echo 545826498093011871441688642479259504041283061123554586469819861859389894946467489199080893852931993824875963703801740289530014752159 | ecm -n -c 3961 11e6

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

echo 545826498093011871441688642479259504041283061123554586469819861859389894946467489199080893852931993824875963703801740289530014752159 | ecm -n -c 7465 43e6

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

echo 545826498093011871441688642479259504041283061123554586469819861859389894946467489199080893852931993824875963703801740289530014752159 | ecm -n -c 17751 11e7

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

echo 545826498093011871441688642479259504041283061123554586469819861859389894946467489199080893852931993824875963703801740289530014752159 | 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