Contribution and Reservation

(13·10¹⁹⁷-31)/9 =: 1(4)₁₉₆1_<198>; = 3 · 11 · 223 · 194684069 · [100821144997472713244138291979019339036213372676439578618544319988591042278809704387909921212720816084558507074897318152809816931631354452760797692042615814553697500167937823683503287771_<186>] SUBMIT/RESERVE

Status

Expression:	(13·10¹⁹⁷-31)/9
Composite Factor:	100821144997472713244138291979019339036213372676439578618544 319988591042278809704387909921212720816084558507074897318152 809816931631354452760797692042615814553697500167937823683503 287771 (186-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 199.02-digit and the GNFS difficulty is 185.00-digit. SNFS must be faster than GNFS. It will take about 18 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 14441_197.
Put the following polynomial file 14441_197.poly in there too.
And then, run "perl factMsieve.pl 14441_197".

14441_197.poly ^*1

n: 100821144997472713244138291979019339036213372676439578618544319988591042278809704387909921212720816084558507074897318152809816931631354452760797692042615814553697500167937823683503287771
m: 2000000000000000000000000000000000000000
deg: 5
c5: 325
c0: -248
skew: 0.95
type: snfs
lss: 1
rlim: 14500000
alim: 14500000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5

*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 186-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	2500	Dmitry Domanov	Jun 18, 2009
40	3e6	2500 / 2350
45	11e6	0 / 3928
45	11e6	/ 3928
50	43e6	0 / 7459 (1120)
50	43e6	/ 7459 (1120)
55	11e7	0 / 17750 (3094)
55	11e7	/ 17750 (3094)
60	26e7	0 / 42014 (7635)
60	26e7	/ 42014 (7635)

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

echo 100821144997472713244138291979019339036213372676439578618544319988591042278809704387909921212720816084558507074897318152809816931631354452760797692042615814553697500167937823683503287771 | ecm -n -c 3928 11e6

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

echo 100821144997472713244138291979019339036213372676439578618544319988591042278809704387909921212720816084558507074897318152809816931631354452760797692042615814553697500167937823683503287771 | ecm -n -c 7459 43e6

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

echo 100821144997472713244138291979019339036213372676439578618544319988591042278809704387909921212720816084558507074897318152809816931631354452760797692042615814553697500167937823683503287771 | ecm -n -c 17750 11e7

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

echo 100821144997472713244138291979019339036213372676439578618544319988591042278809704387909921212720816084558507074897318152809816931631354452760797692042615814553697500167937823683503287771 | ecm -n -c 42014 26e7

Submit factors

Make reservation

Back to Factorizations of near-repdigit numbers