Contribution and Reservation

(16·10¹⁹³+11)/9 =: 1(7)₁₉₂9_<194>; = 31 · 857 · 1327 · 2856283 · 447416443 · 206810811397_<12> · 1933766524667695648360943_<25> · [986673768513915917363314921607718421558314876934280279261747671286087669908468792132162037750488654624333218517931876247311876531214169_<135>] SUBMIT/RESERVE

Status

Expression:	(16·10¹⁹³+11)/9
Composite Factor:	986673768513915917363314921607718421558314876934280279261747 671286087669908468792132162037750488654624333218517931876247 311876531214169 (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 195.11-digit and the GNFS difficulty is 134.99-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 17779_193.
Put the following polynomial file 17779_193.poly in there too.
And then, run "perl factMsieve.pl 17779_193".

17779_193.poly ^*1

# Murphy_E = 3.898479e-11, selected by Jeff Gilchrist
n: 986673768513915917363314921607718421558314876934280279261747671286087669908468792132162037750488654624333218517931876247311876531214169
Y0: -107284011683762931485357735
Y1: 1175679317726221
c0: -1524451911437202574917379977743616
c1: 11540659319901638311584927916
c2: -48977014335594995907078
c3: -41688704214040380
c4: 203470145855
c5: 69420
skew: 659985.53
type: gnfs
# selected mechanically
rlim: 13400000
alim: 13400000
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 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	2336	Wataru Sakai	Apr 20, 2009
40	3e6	2336 / 2336
45	11e6	0 / 3962
45	11e6	/ 3962
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 986673768513915917363314921607718421558314876934280279261747671286087669908468792132162037750488654624333218517931876247311876531214169 | ecm -n -c 3962 11e6

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

echo 986673768513915917363314921607718421558314876934280279261747671286087669908468792132162037750488654624333218517931876247311876531214169 | ecm -n -c 7465 43e6

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

echo 986673768513915917363314921607718421558314876934280279261747671286087669908468792132162037750488654624333218517931876247311876531214169 | ecm -n -c 17751 11e7

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

echo 986673768513915917363314921607718421558314876934280279261747671286087669908468792132162037750488654624333218517931876247311876531214169 | 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