Contribution and Reservation

(25·10¹⁹²-7)/9 =: 2(7)₁₉₂_<193>; = 31 · 40459 · [2214729349885688959335000050052883307416570480971001131195162747614492869944625565010678096087538860748537769241324971578378252916953584853944357671348515923151017699142483372476459863213_<187>] SUBMIT/RESERVE

Status

Expression:	(25·10¹⁹²-7)/9
Composite Factor:	221472934988568895933500005005288330741657048097100113119516 274761449286994462556501067809608753886074853776924132497157 837825291695358485394435767134851592315101769914248337247645 9863213 (187-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 194.10-digit and the GNFS difficulty is 186.35-digit. SNFS must be faster than GNFS. It will take about 12 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 27777_192.
Put the following polynomial file 27777_192.poly in there too.
And then, run "perl factMsieve.pl 27777_192".

27777_192.poly ^*1

n: 2214729349885688959335000050052883307416570480971001131195162747614492869944625565010678096087538860748537769241324971578378252916953584853944357671348515923151017699142483372476459863213
m: 500000000000000000000000000000000000000
deg: 5
c5: 4
c0: -35
skew: 1.54
type: snfs
lss: 1
rlim: 12000000
alim: 12000000
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 187-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	Jul 12, 2009
40	3e6	2500 / 2009
45	11e6	0 / 3871
45	11e6	/ 3871
50	43e6	0 / 7452 (1104)
50	43e6	/ 7452 (1104)
55	11e7	0 / 17749 (3091)
55	11e7	/ 17749 (3091)
60	26e7	0 / 42014 (7635)
60	26e7	/ 42014 (7635)

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

echo 2214729349885688959335000050052883307416570480971001131195162747614492869944625565010678096087538860748537769241324971578378252916953584853944357671348515923151017699142483372476459863213 | ecm -n -c 3871 11e6

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

echo 2214729349885688959335000050052883307416570480971001131195162747614492869944625565010678096087538860748537769241324971578378252916953584853944357671348515923151017699142483372476459863213 | ecm -n -c 7452 43e6

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

echo 2214729349885688959335000050052883307416570480971001131195162747614492869944625565010678096087538860748537769241324971578378252916953584853944357671348515923151017699142483372476459863213 | ecm -n -c 17749 11e7

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

echo 2214729349885688959335000050052883307416570480971001131195162747614492869944625565010678096087538860748537769241324971578378252916953584853944357671348515923151017699142483372476459863213 | ecm -n -c 42014 26e7

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