Contribution and Reservation

(16·10²¹³-1)/3 =: 5(3)₂₁₃_<214>; = 23701159 · [225024157398097423562001053760001075615472362905684626365036972805141441957894689172514024876730008576092558736614244617038910769440993722430761016089269445993477927949993219037656906707951848824495600967587_<207>] SUBMIT/RESERVE

Status

Expression:	(16·10²¹³-1)/3
Composite Factor:	225024157398097423562001053760001075615472362905684626365036 972805141441957894689172514024876730008576092558736614244617 038910769440993722430761016089269445993477927949993219037656 906707951848824495600967587 (207-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 214.20-digit and the GNFS difficulty is 206.35-digit. SNFS must be faster than GNFS. It will take about 58 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 53333_213.
Put the following polynomial file 53333_213.poly in there too.
And then, run "perl factMsieve.pl 53333_213".

53333_213.poly

n: 225024157398097423562001053760001075615472362905684626365036972805141441957894689172514024876730008576092558736614244617038910769440993722430761016089269445993477927949993219037656906707951848824495600967587
m: 200000000000000000000000000000000000
deg: 6
c6: 250
c0: -1
skew: 0.40
type: snfs
lss: 1
rlim: 26000000
alim: 26000000
lpbr: 29
lpba: 29
mfbr: 57
mfba: 57
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 207-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	680	Dmitry Domanov	Dec 18, 2009
		680 / 4479
		/ 3799
50	43e6	0 / 7401 (1083)
50	43e6	/ 7401 (1083)
55	11e7	0 / 17727 (3070)
55	11e7	/ 17727 (3070)
60	26e7	0 / 42007 (7625)
60	26e7	/ 42007 (7625)

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

echo 225024157398097423562001053760001075615472362905684626365036972805141441957894689172514024876730008576092558736614244617038910769440993722430761016089269445993477927949993219037656906707951848824495600967587 | ecm -n -c 3799 11e6

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

echo 225024157398097423562001053760001075615472362905684626365036972805141441957894689172514024876730008576092558736614244617038910769440993722430761016089269445993477927949993219037656906707951848824495600967587 | ecm -n -c 7401 43e6

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

echo 225024157398097423562001053760001075615472362905684626365036972805141441957894689172514024876730008576092558736614244617038910769440993722430761016089269445993477927949993219037656906707951848824495600967587 | ecm -n -c 17727 11e7

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

echo 225024157398097423562001053760001075615472362905684626365036972805141441957894689172514024876730008576092558736614244617038910769440993722430761016089269445993477927949993219037656906707951848824495600967587 | ecm -n -c 42007 26e7

Submit factors

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