Contribution and Reservation

(8·10²²⁷+1)/9 =: (8)₂₂₆9_<227>; = 829 · 23081 · 510625190477286935450849_<24> · [9097793815393447552722809249138055200656158678748957766912186177233971864190349402337867308990770756526315512821678093326066945622035654440878171666227400696434321205697103138583138190600028256389_<196>] SUBMIT/RESERVE

Status

Expression:	(8·10²²⁷+1)/9
Composite Factor:	909779381539344755272280924913805520065615867874895776691218 617723397186419034940233786730899077075652631551282167809332 606694562203565444087817166622740069643432120569710313858313 8190600028256389 (196-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 228.60-digit and the GNFS difficulty is 195.96-digit. SNFS must be faster than GNFS. It will take about 174 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 88889_227.
Put the following polynomial file 88889_227.poly in there too.
And then, run "perl factMsieve.pl 88889_227".

88889_227.poly ^*1

n: 9097793815393447552722809249138055200656158678748957766912186177233971864190349402337867308990770756526315512821678093326066945622035654440878171666227400696434321205697103138583138190600028256389
m: 100000000000000000000000000000000000000
deg: 6
c6: 4
c0: 5
skew: 1.04
type: snfs
lss: 1
rlim: 45000000
alim: 45000000
lpbr: 30
lpba: 30
mfbr: 59
mfba: 59
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 196-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, 2008
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 9097793815393447552722809249138055200656158678748957766912186177233971864190349402337867308990770756526315512821678093326066945622035654440878171666227400696434321205697103138583138190600028256389 | ecm -n -c 825 1e6

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

echo 9097793815393447552722809249138055200656158678748957766912186177233971864190349402337867308990770756526315512821678093326066945622035654440878171666227400696434321205697103138583138190600028256389 | ecm -n -c 2336 3e6

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

echo 9097793815393447552722809249138055200656158678748957766912186177233971864190349402337867308990770756526315512821678093326066945622035654440878171666227400696434321205697103138583138190600028256389 | ecm -n -c 4479 11e6

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

echo 9097793815393447552722809249138055200656158678748957766912186177233971864190349402337867308990770756526315512821678093326066945622035654440878171666227400696434321205697103138583138190600028256389 | ecm -n -c 7553 43e6

Submit factors

Make reservation

Back to Factorizations of near-repdigit numbers