Contribution and Reservation

(10²²¹+53)/9 =: (1)₂₂₀7_<221>; = 373669 · [29735169658470761853702370576930682264547262714089504644782176501425355357578795969457223133605172254351073038199880405147633630595824409065539584795931990909363932012318686086111267220751818082610843048556639997193_<215>] SUBMIT/RESERVE

Status

Expression:	(10²²¹+53)/9
Composite Factor:	297351696584707618537023705769306822645472627140895046447821 765014253553575787959694572231336051722543510730381998804051 476336305958244090655395847959319909093639320123186860861112 67220751818082610843048556639997193 (215-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 221.70-digit and the GNFS difficulty is 214.47-digit. SNFS must be faster than GNFS. It will take about 102 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 11117_221.
Put the following polynomial file 11117_221.poly in there too.
And then, run "perl factMsieve.pl 11117_221".

11117_221.poly ^*1

n: 29735169658470761853702370576930682264547262714089504644782176501425355357578795969457223133605172254351073038199880405147633630595824409065539584795931990909363932012318686086111267220751818082610843048556639997193
m: 5000000000000000000000000000000000000
deg: 6
c6: 32
c0: 265
skew: 1.42
type: snfs
lss: 1
rlim: 35000000
alim: 35000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6

*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 215-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	400	Serge Batalov	Feb 3, 2009
		400 / 2336
		/ 1936
45	11e6	0 / 4390 (561)
45	11e6	/ 4390 (561)
50	43e6	0 / 7538 (1252)
50	43e6	/ 7538 (1252)
55	11e7	0 / 17766 (3127)
55	11e7	/ 17766 (3127)

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

echo 29735169658470761853702370576930682264547262714089504644782176501425355357578795969457223133605172254351073038199880405147633630595824409065539584795931990909363932012318686086111267220751818082610843048556639997193 | ecm -n -c 1936 3e6

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

echo 29735169658470761853702370576930682264547262714089504644782176501425355357578795969457223133605172254351073038199880405147633630595824409065539584795931990909363932012318686086111267220751818082610843048556639997193 | ecm -n -c 4390 11e6

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

echo 29735169658470761853702370576930682264547262714089504644782176501425355357578795969457223133605172254351073038199880405147633630595824409065539584795931990909363932012318686086111267220751818082610843048556639997193 | ecm -n -c 7538 43e6

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

echo 29735169658470761853702370576930682264547262714089504644782176501425355357578795969457223133605172254351073038199880405147633630595824409065539584795931990909363932012318686086111267220751818082610843048556639997193 | ecm -n -c 17766 11e7

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