Contribution and Reservation

9·10²¹⁹-1 =: 8(9)₂₁₉_<220>; = 136523 · 3275933 · [20123414623063055102118571087903749096571159337618260154664291160939792032690128124998976228268348411190796072598184524509069267467017885465416230112288285628875789971268498264586927034423866579944092570018561_<209>] SUBMIT/RESERVE

Status

Expression:	9·10²¹⁹-1
Composite Factor:	201234146230630551021185710879037490965711593376182601546642 911609397920326901281249989762282683484111907960725981845245 090692674670178854654162301122882856288757899712684982645869 27034423866579944092570018561 (209-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 222.05-digit and the GNFS difficulty is 208.30-digit. SNFS must be faster than GNFS. It will take about 105 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 89999_219.
Put the following polynomial file 89999_219.poly in there too.
And then, run "perl factMsieve.pl 89999_219".

89999_219.poly ^*1

n: 20123414623063055102118571087903749096571159337618260154664291160939792032690128124998976228268348411190796072598184524509069267467017885465416230112288285628875789971268498264586927034423866579944092570018561
m: 5000000000000000000000000000000000000
deg: 6
c6: 72
c0: -125
skew: 1.10
type: snfs
lss: 1
rlim: 35000000
alim: 35000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
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 209-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	Oct 31, 2007
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 20123414623063055102118571087903749096571159337618260154664291160939792032690128124998976228268348411190796072598184524509069267467017885465416230112288285628875789971268498264586927034423866579944092570018561 | ecm -n -c 825 1e6

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

echo 20123414623063055102118571087903749096571159337618260154664291160939792032690128124998976228268348411190796072598184524509069267467017885465416230112288285628875789971268498264586927034423866579944092570018561 | ecm -n -c 2336 3e6

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

echo 20123414623063055102118571087903749096571159337618260154664291160939792032690128124998976228268348411190796072598184524509069267467017885465416230112288285628875789971268498264586927034423866579944092570018561 | ecm -n -c 4479 11e6

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

echo 20123414623063055102118571087903749096571159337618260154664291160939792032690128124998976228268348411190796072598184524509069267467017885465416230112288285628875789971268498264586927034423866579944092570018561 | ecm -n -c 7553 43e6

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