Contribution and Reservation

(64·10³⁰⁷-1)/9 =: 7(1)₃₀₇_<308>; = 197 · 1719814763_<10> · 24399198114186200332253_<23> · [8602288672636387264424347165986972855214373111667363325477631024908651985087761144209626404249521977750713234864193691713456956594828975481481628076219458460493612830715286114144279308229111122591964635365633709962316198546052343578679647956331417594539970104848459072280517_<274>] SUBMIT/RESERVE

Status

Expression:	(64·10³⁰⁷-1)/9
Composite Factor:	860228867263638726442434716598697285521437311166736332547763 102490865198508776114420962640424952197775071323486419369171 345695659482897548148162807621945846049361283071528611414427 930822911112259196463536563370996231619854605234357867964795 6331417594539970104848459072280517 (274-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 308.81-digit and the GNFS difficulty is 273.93-digit. SNFS must be faster than GNFS. It will take about 81908 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 71111_307.
Put the following polynomial file 71111_307.poly in there too.
And then, run "perl factMsieve.pl 71111_307".

71111_307.poly ^*1

n: 8602288672636387264424347165986972855214373111667363325477631024908651985087761144209626404249521977750713234864193691713456956594828975481481628076219458460493612830715286114144279308229111122591964635365633709962316198546052343578679647956331417594539970104848459072280517
m: 2000000000000000000000000000000000000000000000000000
deg: 6
c6: 10
c0: -1
skew: 0.68
type: snfs
lss: 1
rlim: 980000000
alim: 980000000
lpbr: 33
lpba: 33
mfbr: 69
mfba: 69
rlambda: 3.0
alambda: 3.0

*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 274-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	600	Serge Batalov	Feb 16, 2009
40	3e6	600 / 62
45	11e6	600	Serge Batalov	Feb 16, 2009
		600 / 4311
		/ 3711
50	43e6	0 / 7391 (1058)
50	43e6	/ 7391 (1058)
55	11e7	0 / 17726 (3066)
55	11e7	/ 17726 (3066)
60	26e7	0 / 42007 (7625)
60	26e7	/ 42007 (7625)

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

echo 8602288672636387264424347165986972855214373111667363325477631024908651985087761144209626404249521977750713234864193691713456956594828975481481628076219458460493612830715286114144279308229111122591964635365633709962316198546052343578679647956331417594539970104848459072280517 | ecm -n -c 3711 11e6

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

echo 8602288672636387264424347165986972855214373111667363325477631024908651985087761144209626404249521977750713234864193691713456956594828975481481628076219458460493612830715286114144279308229111122591964635365633709962316198546052343578679647956331417594539970104848459072280517 | ecm -n -c 7391 43e6

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

echo 8602288672636387264424347165986972855214373111667363325477631024908651985087761144209626404249521977750713234864193691713456956594828975481481628076219458460493612830715286114144279308229111122591964635365633709962316198546052343578679647956331417594539970104848459072280517 | ecm -n -c 17726 11e7

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

echo 8602288672636387264424347165986972855214373111667363325477631024908651985087761144209626404249521977750713234864193691713456956594828975481481628076219458460493612830715286114144279308229111122591964635365633709962316198546052343578679647956331417594539970104848459072280517 | ecm -n -c 42007 26e7

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