Contribution and Reservation

(43·10²⁴¹-7)/9 =: 4(7)₂₄₁_<242>; = 29 · 1663 · 3557 · 7590571 · 205100619677_<12> · 902516608090556639_<18> · [198223532756400302423637525534117173338210316114197781973050289877433828713313297290713944681056203369162992488600070742658514300826633740713236889577183394140618186908901800210841008013753846190911_<198>] SUBMIT/RESERVE

Status

Expression:	(43·10²⁴¹-7)/9
Composite Factor:	198223532756400302423637525534117173338210316114197781973050 289877433828713313297290713944681056203369162992488600070742 658514300826633740713236889577183394140618186908901800210841 008013753846190911 (198-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.

SNFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 244.14-digit and the GNFS difficulty is 197.30-digit. SNFS must be faster than GNFS. It will take about 572 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 47777_241.
Put the following polynomial file 47777_241.poly in there too.
And then, run "perl factMsieve.pl 47777_241".

47777_241.poly ^*1

n: 198223532756400302423637525534117173338210316114197781973050289877433828713313297290713944681056203369162992488600070742658514300826633740713236889577183394140618186908901800210841008013753846190911
m: 20000000000000000000000000000000000000000
deg: 6
c6: 215
c0: -224
skew: 1.01
type: snfs
lss: 1
rlim: 82000000
alim: 82000000
lpbr: 30
lpba: 30
mfbr: 61
mfba: 61
rlambda: 2.7
alambda: 2.7

*1 These parameters were not fully adjusted. The approximate expressions which were used for making the parameters are: deg=expt<=105?4:expt<=210?5:6 or expt<=144?4:6; d=log10(c[deg])+deg*log10(m)[digits]; time=10^(d/30-4)[hours]; skew=|c0/c[deg]|^(1/deg); rlim=round(7*10^(d/60+3)); lpbr=floor(d/25+21); mfbr=floor(d/8+31); rlambda=floor(d/25+18)/10;

Efforts by ECM

The efforts by ECM to find small factors of this 198-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 30-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
30	25e4	430	Makoto Kamada	Jan 27, 2009
30	25e4	430 / 430
35	1e6	0 / 825
35	1e6	/ 825
40	3e6	0 / 2336 (294)
40	3e6	/ 2336 (294)
45	11e6	0 / 4479 (677)
45	11e6	/ 4479 (677)
50	43e6	0 / 7553 (1277)
50	43e6	/ 7553 (1277)

Command line to find prime factors up to about 35-digit

echo 198223532756400302423637525534117173338210316114197781973050289877433828713313297290713944681056203369162992488600070742658514300826633740713236889577183394140618186908901800210841008013753846190911 | ecm -n -c 825 1e6

Command line to find prime factors up to about 40-digit

echo 198223532756400302423637525534117173338210316114197781973050289877433828713313297290713944681056203369162992488600070742658514300826633740713236889577183394140618186908901800210841008013753846190911 | ecm -n -c 2336 3e6

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

echo 198223532756400302423637525534117173338210316114197781973050289877433828713313297290713944681056203369162992488600070742658514300826633740713236889577183394140618186908901800210841008013753846190911 | ecm -n -c 4479 11e6

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

echo 198223532756400302423637525534117173338210316114197781973050289877433828713313297290713944681056203369162992488600070742658514300826633740713236889577183394140618186908901800210841008013753846190911 | ecm -n -c 7553 43e6

Submit factors

Make reservation

Back to Factorizations of near-repdigit numbers