Contribution and Reservation

(19·10¹⁹⁷-1)/9 =: 2(1)₁₉₇_<198>; = 217409 · 148309607497483921_<18> · 39352703424498545120297305189_<29> · [166375630748703395463164557225749379129853263886867234344540086253317490155678563790257803512283631412627990637610456181042880430192706837121126091_<147>] (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=2585434931 for P29 / Oct 21, 2008) SUBMIT/RESERVE

Status

Expression:	(19·10¹⁹⁷-1)/9
Composite Factor:	166375630748703395463164557225749379129853263886867234344540 086253317490155678563790257803512283631412627990637610456181 042880430192706837121126091 (147-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 200.38-digit and the GNFS difficulty is 146.22-digit. SNFS must be faster than GNFS. It will take about 20 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 21111_197.
Put the following polynomial file 21111_197.poly in there too.
And then, run "perl factMsieve.pl 21111_197".

21111_197.poly ^*1

n: 166375630748703395463164557225749379129853263886867234344540086253317490155678563790257803512283631412627990637610456181042880430192706837121126091
m: 5000000000000000000000000000000000000000
deg: 5
c5: 76
c0: -125
skew: 1.10
type: snfs
lss: 1
rlim: 15300000
alim: 15300000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6

*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 147-digit composite number are not reported yet. Please report your efforts by ECM. (Anonymous reports are not acceptable)

Level	B1	Reported runs Total / Required runs (Required runs for lower level)
20	11e3	0 / 74
20	11e3	/ 74
25	5e4	0 / 214 (21)
25	5e4	/ 214 (21)
30	25e4	0 / 430 (50)
30	25e4	/ 430 (50)
35	1e6	0 / 904 (118)
35	1e6	/ 904 (118)
40	3e6	0 / 2350 (322)
40	3e6	/ 2350 (322)

Command line to find prime factors up to about 20-digit

echo 166375630748703395463164557225749379129853263886867234344540086253317490155678563790257803512283631412627990637610456181042880430192706837121126091 | ecm -n -c 74 11e3

Command line to find prime factors up to about 25-digit

echo 166375630748703395463164557225749379129853263886867234344540086253317490155678563790257803512283631412627990637610456181042880430192706837121126091 | ecm -n -c 214 5e4

Command line to find prime factors up to about 30-digit

echo 166375630748703395463164557225749379129853263886867234344540086253317490155678563790257803512283631412627990637610456181042880430192706837121126091 | ecm -n -c 430 25e4

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

echo 166375630748703395463164557225749379129853263886867234344540086253317490155678563790257803512283631412627990637610456181042880430192706837121126091 | ecm -n -c 904 1e6

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

echo 166375630748703395463164557225749379129853263886867234344540086253317490155678563790257803512283631412627990637610456181042880430192706837121126091 | ecm -n -c 2350 3e6

Submit factors

Make reservation

Back to Factorizations of near-repdigit numbers