Contribution and Reservation

(22·10¹⁸⁶-1)/3 =: 7(3)₁₈₆_<187>; = 7 · 67 · 331 · 5679860644357315055141531091607_<31> · [8316927375912425675232689124341181802299980314993069805942537621415770313404508190180998100214135140699510365051647362171567079564114595515698728073621_<151>] (Wataru Sakai / GMP-ECM 6.1 B1=11000000, sigma=272521171 for P31 / Dec 25, 2006) SUBMIT/RESERVE

Status

Expression:	(22·10¹⁸⁶-1)/3
Composite Factor:	831692737591242567523268912434118180229998031499306980594253 762141577031340450819018099810021413514069951036505164736217 1567079564114595515698728073621 (151-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 188.25-digit and the GNFS difficulty is 150.92-digit. SNFS must be faster than GNFS. It will take about 8 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 73333_186.
Put the following polynomial file 73333_186.poly in there too.
And then, run "perl factMsieve.pl 73333_186".

73333_186.poly ^*1

n: 8316927375912425675232689124341181802299980314993069805942537621415770313404508190180998100214135140699510365051647362171567079564114595515698728073621
m: 20000000000000000000000000000000000000
deg: 5
c5: 55
c0: -8
skew: 0.68
type: snfs
lss: 1
rlim: 9600000
alim: 9600000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5

*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 151-digit composite number are not reported yet. Please report your efforts by ECM. (Anonymous reports are not acceptable)

Level	B1	Reported runs Total / Required runs (Required runs for lower level)
20	11e3	0 / 74
20	11e3	/ 74
25	5e4	0 / 214 (21)
25	5e4	/ 214 (21)
30	25e4	0 / 430 (50)
30	25e4	/ 430 (50)
35	1e6	0 / 904 (118)
35	1e6	/ 904 (118)
40	3e6	0 / 2350 (322)
40	3e6	/ 2350 (322)

Command line to find prime factors up to about 20-digit

echo 8316927375912425675232689124341181802299980314993069805942537621415770313404508190180998100214135140699510365051647362171567079564114595515698728073621 | ecm -n -c 74 11e3

Command line to find prime factors up to about 25-digit

echo 8316927375912425675232689124341181802299980314993069805942537621415770313404508190180998100214135140699510365051647362171567079564114595515698728073621 | ecm -n -c 214 5e4

Command line to find prime factors up to about 30-digit

echo 8316927375912425675232689124341181802299980314993069805942537621415770313404508190180998100214135140699510365051647362171567079564114595515698728073621 | ecm -n -c 430 25e4

Command line to find prime factors up to about 35-digit

echo 8316927375912425675232689124341181802299980314993069805942537621415770313404508190180998100214135140699510365051647362171567079564114595515698728073621 | ecm -n -c 904 1e6

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

echo 8316927375912425675232689124341181802299980314993069805942537621415770313404508190180998100214135140699510365051647362171567079564114595515698728073621 | ecm -n -c 2350 3e6

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