Contribution and Reservation

(8·10²²¹+1)/9 =: (8)₂₂₀9_<221>; = 83 · 47303 · [22640222999404477234279414481948822851320438650924580011835742578513675586150420905800795866099042315737097315687430326482486754549786289030011058899926846609461049208496388926882013109764527247664031316409257236261_<215>] SUBMIT/RESERVE

Status

Expression:	(8·10²²¹+1)/9
Composite Factor:	226402229994044772342794144819488228513204386509245800118357 425785136755861504209058007958660990423157370973156874303264 824867545497862890300110588999268466094610492084963889268820 13109764527247664031316409257236261 (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.

NFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 221.90-digit and the GNFS difficulty is 214.35-digit. SNFS must be faster than GNFS. It will take about 104 CPU-days to factor this composite number on 64-bit Opteron-2600MHz.

Steps of SNFS

Put factMsieve.pl to which $GGNFS_BIN_PATH and $NUM_CPUS were modified properly in the working directory 88889_221.
Put the following polynomial file 88889_221.poly in there too.
And then, run "perl factMsieve.pl 88889_221".

88889_221.poly

n: 22640222999404477234279414481948822851320438650924580011835742578513675586150420905800795866099042315737097315687430326482486754549786289030011058899926846609461049208496388926882013109764527247664031316409257236261
m: 2000000000000000000000000000000000000
deg: 6
c6: 12500
c0: 1
skew: 0.21
type: snfs
lss: 1
rlim: 35000000
alim: 35000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6

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 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	280	Serge Batalov	Nov 14, 2008
		20	Serge Batalov	Nov 14, 2008
		300 / 0
45	11e6	572	Dmitry Domanov	Dec 20, 2009
		700	Dmitry Domanov	Jan 8, 2010
		1272 / 4413
		/ 3141
50	43e6	0 / 7257 (896)
50	43e6	/ 7257 (896)
55	11e7	0 / 17688 (3010)
55	11e7	/ 17688 (3010)
60	26e7	0 / 41997 (7608)
60	26e7	/ 41997 (7608)

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

echo 22640222999404477234279414481948822851320438650924580011835742578513675586150420905800795866099042315737097315687430326482486754549786289030011058899926846609461049208496388926882013109764527247664031316409257236261 | ecm -n -c 3141 11e6

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

echo 22640222999404477234279414481948822851320438650924580011835742578513675586150420905800795866099042315737097315687430326482486754549786289030011058899926846609461049208496388926882013109764527247664031316409257236261 | ecm -n -c 7257 43e6

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

echo 22640222999404477234279414481948822851320438650924580011835742578513675586150420905800795866099042315737097315687430326482486754549786289030011058899926846609461049208496388926882013109764527247664031316409257236261 | ecm -n -c 17688 11e7

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

echo 22640222999404477234279414481948822851320438650924580011835742578513675586150420905800795866099042315737097315687430326482486754549786289030011058899926846609461049208496388926882013109764527247664031316409257236261 | ecm -n -c 41997 26e7

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