Contribution and Reservation

(17·10¹⁸⁹-71)/9 =: 1(8)₁₈₈1_<190>; = 3 · 11 · 23 · 619 · 739 · 5279210203_<10> · 13409604493_<11> · 107675266350465140830705193009_<30> · [713721320572161835952425940821028245908329503806862456004886005577420054467244827323363096684513978748912648200246868295107834390009_<132>] (Makoto Kamada / GMP-ECM 5.0.3 B1=4000000, sigma=1448624200 for P30) SUBMIT/RESERVE

Status

Expression:	(17·10¹⁸⁹-71)/9
Composite Factor:	713721320572161835952425940821028245908329503806862456004886 005577420054467244827323363096684513978748912648200246868295 107834390009 (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 190.93-digit and the GNFS difficulty is 131.85-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_189.
Put the following polynomial file 18881_189.poly in there too.
And then, run "perl factMsieve.pl 18881_189".

18881_189.poly ^*1

# Murphy_E = 5.797036e-11, selected by Jeff Gilchrist
n: 713721320572161835952425940821028245908329503806862456004886005577420054467244827323363096684513978748912648200246868295107834390009
Y0: -28652183410887410035588171
Y1: 317793407991319
c0: 6537313475225493200195116235302440
c1: 10141261145012899849966804758
c2: -40876528785956901685957
c3: -70815387709483586
c4: 62114583200
c5: 36960
skew: 903795.19
type: gnfs
# selected mechanically
rlim: 11000000
alim: 11000000
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 713721320572161835952425940821028245908329503806862456004886005577420054467244827323363096684513978748912648200246868295107834390009 | ecm -n -c 3961 11e6

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

echo 713721320572161835952425940821028245908329503806862456004886005577420054467244827323363096684513978748912648200246868295107834390009 | ecm -n -c 7465 43e6

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

echo 713721320572161835952425940821028245908329503806862456004886005577420054467244827323363096684513978748912648200246868295107834390009 | ecm -n -c 17751 11e7

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

echo 713721320572161835952425940821028245908329503806862456004886005577420054467244827323363096684513978748912648200246868295107834390009 | 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