Contribution and Reservation

(16·10²⁴⁰-7)/9 =: 1(7)₂₄₀_<241>; = 47 · 3409729 · 10171093 · 13765051 · 36580939 · [2166004988958189883190393134036989085577139350353818201910584557972751217274085520360072306147358576374538080264992064863981003105920566571983007436016858718965772493609946075188210716467752822204056249398780427_<211>] SUBMIT/RESERVE

Status

Expression:	(16·10²⁴⁰-7)/9
Composite Factor:	216600498895818988319039313403698908557713935035381820191058 455797275121727408552036007230614735857637453808026499206486 398100310592056657198300743601685871896577249360994607518821 0716467752822204056249398780427 (211-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 241.20-digit and the GNFS difficulty is 210.34-digit. SNFS must be faster than GNFS. It will take about 457 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 17777_240.
Put the following polynomial file 17777_240.poly in there too.
And then, run "perl factMsieve.pl 17777_240".

17777_240.poly ^*1

n: 2166004988958189883190393134036989085577139350353818201910584557972751217274085520360072306147358576374538080264992064863981003105920566571983007436016858718965772493609946075188210716467752822204056249398780427
m: 10000000000000000000000000000000000000000
deg: 6
c6: 16
c0: -7
skew: 0.87
type: snfs
lss: 1
rlim: 73000000
alim: 73000000
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 211-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 45-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
45	11e6	4500	Dmitry Domanov	Sep 2, 2009
45	11e6	4500 / 3856
50	43e6	0 / 6439
50	43e6	/ 6439
55	11e7	0 / 17466 (2671)
55	11e7	/ 17466 (2671)
60	26e7	0 / 41942 (7513)
60	26e7	/ 41942 (7513)
65	85e7	0 / 69396 (13587)
65	85e7	/ 69396 (13587)

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

echo 2166004988958189883190393134036989085577139350353818201910584557972751217274085520360072306147358576374538080264992064863981003105920566571983007436016858718965772493609946075188210716467752822204056249398780427 | ecm -n -c 6439 43e6

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

echo 2166004988958189883190393134036989085577139350353818201910584557972751217274085520360072306147358576374538080264992064863981003105920566571983007436016858718965772493609946075188210716467752822204056249398780427 | ecm -n -c 17466 11e7

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

echo 2166004988958189883190393134036989085577139350353818201910584557972751217274085520360072306147358576374538080264992064863981003105920566571983007436016858718965772493609946075188210716467752822204056249398780427 | ecm -n -c 41942 26e7

Command line to find prime factors up to about 65-digit

echo 2166004988958189883190393134036989085577139350353818201910584557972751217274085520360072306147358576374538080264992064863981003105920566571983007436016858718965772493609946075188210716467752822204056249398780427 | ecm -n -c 69396 85e7

Submit factors

Make reservation

Back to Factorizations of near-repdigit numbers