Contribution and Reservation

(52·10¹⁸⁵-7)/9 =: 5(7)₁₈₅_<186>; = 17 · 53 · 2157921737_<10> · 40246436214681691411_<20> · 1154328949285905116197937_<25> · [6396513724147418986787843057489983083683214893804746716757458044969417452154763989045919149613724615539447232837304925046558464103_<130>] SUBMIT/RESERVE

Status

Expression:	(52·10¹⁸⁵-7)/9
Composite Factor:	639651372414741898678784305748998308368321489380474671675745 804496941745215476398904591914961372461553944723283730492504 6558464103 (130-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.

GNFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 186.72-digit and the GNFS difficulty is 129.81-digit. GNFS may be faster than SNFS. It will take about 6 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 57777_185.
Put the following polynomial file 57777_185.poly in there too.
And then, run "perl factMsieve.pl 57777_185".

57777_185.poly ^*1

# Murphy_E = 8.320594e-11, selected by Jeff Gilchrist
n: 6396513724147418986787843057489983083683214893804746716757458044969417452154763989045919149613724615539447232837304925046558464103
Y0: -11159432689589908354333140
Y1: 202690305401291
c0: 31814328079252524875287633120013
c1: 1720246468067542659740603966
c2: -610509175387367684459
c3: -18430617573940936
c4: 3694804856
c5: 36960
skew: 440084.02
type: gnfs
# selected mechanically
rlim: 9700000
alim: 9700000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5

*1 These parameters were not fully adjusted. The approximate expressions which were used for making the parameters are: d=log10(n); time=10^(d/21-4)[hours]; rlim=round(3*10^(d/37+3)); lpbr=floor(d/18+21); mfbr=floor(d/5+28); rlambda=floor(d/26+21)/10;

Efforts by ECM

The efforts by ECM to find small factors of this 130-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	500	Erik Branger	Feb 1, 2009
		1850	Wataru Sakai	Aug 8, 2009
		2350 / 2350
45	11e6	0 / 3961
45	11e6	/ 3961
50	43e6	0 / 7465 (1129)
50	43e6	/ 7465 (1129)
55	11e7	0 / 17751 (3097)
55	11e7	/ 17751 (3097)
60	26e7	0 / 42014 (7636)
60	26e7	/ 42014 (7636)

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

echo 6396513724147418986787843057489983083683214893804746716757458044969417452154763989045919149613724615539447232837304925046558464103 | ecm -n -c 3961 11e6

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

echo 6396513724147418986787843057489983083683214893804746716757458044969417452154763989045919149613724615539447232837304925046558464103 | ecm -n -c 7465 43e6

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

echo 6396513724147418986787843057489983083683214893804746716757458044969417452154763989045919149613724615539447232837304925046558464103 | ecm -n -c 17751 11e7

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

echo 6396513724147418986787843057489983083683214893804746716757458044969417452154763989045919149613724615539447232837304925046558464103 | ecm -n -c 42014 26e7

Contribution and Reservation

Status

How to factor it

ECM, P-1, P+1

GNFS

See also

Efforts by ECM

Submit polynomial for GNFS

Submit factors

Make reservation