Contribution and Reservation

10²⁴³-9 =: (9)₂₄₂1_<243>; = 191 · 2090131151_<10> · [2504915584716261518622320429705615928866391516777126140829517966298849095597766181911340323777630907153032718173656534716342455075023976067357210592911756418684539249136127860441745194251162339410637980622953565801313394779101714151_<232>] SUBMIT/RESERVE

Status

Expression:	10²⁴³-9
Composite Factor:	250491558471626151862232042970561592886639151677712614082951 796629884909559776618191134032377763090715303271817365653471 634245507502397606735721059291175641868453924913612786044174 5194251162339410637980622953565801313394779101714151 (232-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 243.90-digit and the GNFS difficulty is 231.40-digit. SNFS must be faster than GNFS. It will take about 562 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 99991_243.
Put the following polynomial file 99991_243.poly in there too.
And then, run "perl factMsieve.pl 99991_243".

99991_243.poly ^*1

n: 2504915584716261518622320429705615928866391516777126140829517966298849095597766181911340323777630907153032718173656534716342455075023976067357210592911756418684539249136127860441745194251162339410637980622953565801313394779101714151
m: 20000000000000000000000000000000000000000
deg: 6
c6: 125
c0: -72
skew: 0.91
type: snfs
lss: 1
rlim: 81000000
alim: 81000000
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 232-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	0 / 0
45	11e6	712	Dmitry Domanov	Jun 30, 2009
		712 / 4479
		/ 3767
50	43e6	0 / 7394 (1074)
50	43e6	/ 7394 (1074)
55	11e7	0 / 17725 (3067)
55	11e7	/ 17725 (3067)
60	26e7	0 / 42006 (7624)
60	26e7	/ 42006 (7624)

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

echo 2504915584716261518622320429705615928866391516777126140829517966298849095597766181911340323777630907153032718173656534716342455075023976067357210592911756418684539249136127860441745194251162339410637980622953565801313394779101714151 | ecm -n -c 3767 11e6

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

echo 2504915584716261518622320429705615928866391516777126140829517966298849095597766181911340323777630907153032718173656534716342455075023976067357210592911756418684539249136127860441745194251162339410637980622953565801313394779101714151 | ecm -n -c 7394 43e6

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

echo 2504915584716261518622320429705615928866391516777126140829517966298849095597766181911340323777630907153032718173656534716342455075023976067357210592911756418684539249136127860441745194251162339410637980622953565801313394779101714151 | ecm -n -c 17725 11e7

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

echo 2504915584716261518622320429705615928866391516777126140829517966298849095597766181911340323777630907153032718173656534716342455075023976067357210592911756418684539249136127860441745194251162339410637980622953565801313394779101714151 | ecm -n -c 42006 26e7

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