Contribution and Reservation

(7·10²¹⁵-43)/9 =: (7)₂₁₄3_<215>; = 2081 · 1504051683081685150327_<22> · 4344239786129705012158373_<25> · 3024223307536720085994159843093307_<34> · [1891442074356078127435530811303209306810261564412542247972987797125896592894268399142579972662858268228984818353299092343914997992589_<133>] (Serge Batalov / GMP-ECM 6.2.3 B1=1000000, sigma=3496836667 for P34 / Jun 1, 2009) SUBMIT/RESERVE

Status

Expression:	(7·10²¹⁵-43)/9
Composite Factor:	189144207435607812743553081130320930681026156441254224797298 779712589659289426839914257997266285826822898481835329909234 3914997992589 (133-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 216.54-digit and the GNFS difficulty is 132.28-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 77773_215.
Put the following polynomial file 77773_215.poly in there too.
And then, run "perl factMsieve.pl 77773_215".

77773_215.poly ^*1

# Murphy_E = 5.585441e-11, selected by Jeff Gilchrist
n: 1891442074356078127435530811303209306810261564412542247972987797125896592894268399142579972662858268228984818353299092343914997992589
Y0: -28753196669212767805967472
Y1: 533895942341003
c0: 69273206979804201420101961325175
c1: 1078248522433193681327382280
c2: -2871511884496871791963
c3: -63026344824218344
c4: 80639299412
c5: 96240
skew: 271298.22
type: gnfs
# selected mechanically
rlim: 11300000
alim: 11300000
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 133-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	2318	Wataru Sakai	Jun 19, 2009
40	3e6	2318 / 2318
45	11e6	0 / 3963
45	11e6	/ 3963
50	43e6	0 / 7465 (1130)
50	43e6	/ 7465 (1130)
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 1891442074356078127435530811303209306810261564412542247972987797125896592894268399142579972662858268228984818353299092343914997992589 | ecm -n -c 3963 11e6

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

echo 1891442074356078127435530811303209306810261564412542247972987797125896592894268399142579972662858268228984818353299092343914997992589 | ecm -n -c 7465 43e6

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

echo 1891442074356078127435530811303209306810261564412542247972987797125896592894268399142579972662858268228984818353299092343914997992589 | ecm -n -c 17751 11e7

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

echo 1891442074356078127435530811303209306810261564412542247972987797125896592894268399142579972662858268228984818353299092343914997992589 | 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