Contribution and Reservation

(8·10²⁴⁸+1)/9 =: (8)₂₄₇9_<248>; = 853647521741015059855267_<24> · [104128327705561543944931510347175093586276681018588879317229309027845086070462881772026811950472282549171380984313090893055479588264997354436791371692423068005894007866833280708963730259493917032855339318439724897216879358067_<225>] SUBMIT/RESERVE

Status

Expression:	(8·10²⁴⁸+1)/9
Composite Factor:	104128327705561543944931510347175093586276681018588879317229 309027845086070462881772026811950472282549171380984313090893 055479588264997354436791371692423068005894007866833280708963 730259493917032855339318439724897216879358067 (225-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 249.20-digit and the GNFS difficulty is 224.02-digit. SNFS must be faster than GNFS. It will take about 844 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_248.
Put the following polynomial file 88889_248.poly in there too.
And then, run "perl factMsieve.pl 88889_248".

88889_248.poly ^*1

n: 104128327705561543944931510347175093586276681018588879317229309027845086070462881772026811950472282549171380984313090893055479588264997354436791371692423068005894007866833280708963730259493917032855339318439724897216879358067
m: 200000000000000000000000000000000000000000
deg: 6
c6: 25
c0: 2
skew: 0.66
type: snfs
lss: 1
rlim: 100000000
alim: 100000000
lpbr: 30
lpba: 30
mfbr: 62
mfba: 62
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 225-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 35-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
35	1e6	0 / 0
40	3e6	0 / 266
40	3e6	/ 266
45	11e6	600	Dmitry Domanov	May 13, 2009
		600 / 4479 (677)
		/ 3879 (77)
50	43e6	0 / 7419 (1106)
50	43e6	/ 7419 (1106)
55	11e7	0 / 17732 (3078)
55	11e7	/ 17732 (3078)

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

echo 104128327705561543944931510347175093586276681018588879317229309027845086070462881772026811950472282549171380984313090893055479588264997354436791371692423068005894007866833280708963730259493917032855339318439724897216879358067 | ecm -n -c 266 3e6

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

echo 104128327705561543944931510347175093586276681018588879317229309027845086070462881772026811950472282549171380984313090893055479588264997354436791371692423068005894007866833280708963730259493917032855339318439724897216879358067 | ecm -n -c 3879 11e6

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

echo 104128327705561543944931510347175093586276681018588879317229309027845086070462881772026811950472282549171380984313090893055479588264997354436791371692423068005894007866833280708963730259493917032855339318439724897216879358067 | ecm -n -c 7419 43e6

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

echo 104128327705561543944931510347175093586276681018588879317229309027845086070462881772026811950472282549171380984313090893055479588264997354436791371692423068005894007866833280708963730259493917032855339318439724897216879358067 | ecm -n -c 17732 11e7

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