Contribution and Reservation

3·10¹⁹¹-1 =: 2(9)₁₉₁_<192>; = 7 · 359 · 1301 · 281993 · 2790288133_<10> · 23268995217971929_<17> · 13515484787040813847_<20> · [370812897556704338509590133832163695071597917566000336371183993274408395233490200784926313895161253111564845043776594915089730392839809_<135>] SUBMIT/RESERVE

Status

Expression:	3·10¹⁹¹-1
Composite Factor:	370812897556704338509590133832163695071597917566000336371183 993274408395233490200784926313895161253111564845043776594915 089730392839809 (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 192.68-digit and the GNFS difficulty is 134.57-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 29999_191.
Put the following polynomial file 29999_191.poly in there too.
And then, run "perl factMsieve.pl 29999_191".

29999_191.poly ^*1

# Murphy_E = 4.225972e-11, selected by Jeff Gilchrist
n: 370812897556704338509590133832163695071597917566000336371183993274408395233490200784926313895161253111564845043776594915089730392839809
Y0: -87896469146934327315300801
Y1: 1026173525582261
c0: -1568176629499857450398904266174800
c1: 19364258004082821259095613780
c2: -18064497583289826231044
c3: -102225741472540897
c4: 15930062250
c5: 70680
skew: 672337.21
type: gnfs
# selected mechanically
rlim: 13000000
alim: 13000000
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	500	Erik Branger	Feb 1, 2009
		1850	Wataru Sakai	Aug 31, 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 370812897556704338509590133832163695071597917566000336371183993274408395233490200784926313895161253111564845043776594915089730392839809 | ecm -n -c 3961 11e6

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

echo 370812897556704338509590133832163695071597917566000336371183993274408395233490200784926313895161253111564845043776594915089730392839809 | ecm -n -c 7465 43e6

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

echo 370812897556704338509590133832163695071597917566000336371183993274408395233490200784926313895161253111564845043776594915089730392839809 | ecm -n -c 17751 11e7

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

echo 370812897556704338509590133832163695071597917566000336371183993274408395233490200784926313895161253111564845043776594915089730392839809 | 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