Contribution and Reservation

(4·10²²¹-1)/3 =: 1(3)₂₂₁_<222>; = 373 · [357462019660411081322609472743521000893655049151027703306523681858802502234137622877569258266309204647006255585344057193923145665773011617515638963360142984807864164432529043789097408400357462019660411081322609472743521_<219>] SUBMIT/RESERVE

Status

Expression:	(4·10²²¹-1)/3
Composite Factor:	357462019660411081322609472743521000893655049151027703306523 681858802502234137622877569258266309204647006255585344057193 923145665773011617515638963360142984807864164432529043789097 408400357462019660411081322609472743521 (219-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 222.30-digit and the GNFS difficulty is 218.55-digit. SNFS must be faster than GNFS. It will take about 107 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 13333_221.
Put the following polynomial file 13333_221.poly in there too.
And then, run "perl factMsieve.pl 13333_221".

13333_221.poly ^*1

n: 357462019660411081322609472743521000893655049151027703306523681858802502234137622877569258266309204647006255585344057193923145665773011617515638963360142984807864164432529043789097408400357462019660411081322609472743521
m: 10000000000000000000000000000000000000
deg: 6
c6: 2
c0: -5
skew: 1.16
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 219-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	2365	Serge Batalov	Sep 9, 2008
		18	Luigi Morelli	Jan 28, 2009
		2383 / 0
50	43e6	1390	Wataru Sakai	Oct 15, 2009
		1390 / 6924
		/ 5534
55	11e7	0 / 17105 (2296)
55	11e7	/ 17105 (2296)
60	26e7	0 / 41813 (7358)
60	26e7	/ 41813 (7358)
65	85e7	0 / 69368 (13545)
65	85e7	/ 69368 (13545)

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

echo 357462019660411081322609472743521000893655049151027703306523681858802502234137622877569258266309204647006255585344057193923145665773011617515638963360142984807864164432529043789097408400357462019660411081322609472743521 | ecm -n -c 5534 43e6

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

echo 357462019660411081322609472743521000893655049151027703306523681858802502234137622877569258266309204647006255585344057193923145665773011617515638963360142984807864164432529043789097408400357462019660411081322609472743521 | ecm -n -c 17105 11e7

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

echo 357462019660411081322609472743521000893655049151027703306523681858802502234137622877569258266309204647006255585344057193923145665773011617515638963360142984807864164432529043789097408400357462019660411081322609472743521 | ecm -n -c 41813 26e7

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

echo 357462019660411081322609472743521000893655049151027703306523681858802502234137622877569258266309204647006255585344057193923145665773011617515638963360142984807864164432529043789097408400357462019660411081322609472743521 | ecm -n -c 69368 85e7

Submit factors

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