Contribution and Reservation

9·10²⁴³-1 =: 8(9)₂₄₃_<244>; = 21874481 · [411438333096908676370424514300476431875115117016947739240076141692230320801668391583782033502874879637144305275174300135395212348123825200698476000413449809392049118788235478592612094430949013144586150409694291718281224592254325942636079_<237>] SUBMIT/RESERVE

Status

Expression:	9·10²⁴³-1
Composite Factor:	411438333096908676370424514300476431875115117016947739240076 141692230320801668391583782033502874879637144305275174300135 395212348123825200698476000413449809392049118788235478592612 094430949013144586150409694291718281224592254325942636079 (237-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 246.05-digit and the GNFS difficulty is 236.61-digit. SNFS must be faster than GNFS. It will take about 663 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_243.
Put the following polynomial file 89999_243.poly in there too.
And then, run "perl factMsieve.pl 89999_243".

89999_243.poly ^*1

n: 411438333096908676370424514300476431875115117016947739240076141692230320801668391583782033502874879637144305275174300135395212348123825200698476000413449809392049118788235478592612094430949013144586150409694291718281224592254325942636079
m: 50000000000000000000000000000000000000000
deg: 6
c6: 72
c0: -125
skew: 1.10
type: snfs
lss: 1
rlim: 88000000
alim: 88000000
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 237-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	2200	Serge Batalov	Jan 1, 2009
		2213	Jo Yeong Uk	Mar 4, 2009
		4413 / 4413
50	43e6	0 / 6552
50	43e6	/ 6552
55	11e7	0 / 17491 (2718)
55	11e7	/ 17491 (2718)
60	26e7	0 / 41947 (7524)
60	26e7	/ 41947 (7524)
65	85e7	0 / 69397 (13589)
65	85e7	/ 69397 (13589)

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

echo 411438333096908676370424514300476431875115117016947739240076141692230320801668391583782033502874879637144305275174300135395212348123825200698476000413449809392049118788235478592612094430949013144586150409694291718281224592254325942636079 | ecm -n -c 6552 43e6

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

echo 411438333096908676370424514300476431875115117016947739240076141692230320801668391583782033502874879637144305275174300135395212348123825200698476000413449809392049118788235478592612094430949013144586150409694291718281224592254325942636079 | ecm -n -c 17491 11e7

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

echo 411438333096908676370424514300476431875115117016947739240076141692230320801668391583782033502874879637144305275174300135395212348123825200698476000413449809392049118788235478592612094430949013144586150409694291718281224592254325942636079 | ecm -n -c 41947 26e7

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

echo 411438333096908676370424514300476431875115117016947739240076141692230320801668391583782033502874879637144305275174300135395212348123825200698476000413449809392049118788235478592612094430949013144586150409694291718281224592254325942636079 | ecm -n -c 69397 85e7

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