Contribution and Reservation

(55·10¹⁸⁸+53)/9 =: 6(1)₁₈₇7_<189>; = 19 · 12401 · 49253 · 230647 · 10409761 · 72209954717_<11> · 146111180767_<12> · 619823757978091241_<18> · [3353820943824522620537912372760719231417658842015843290513910034118943337449091236544542093712213209484684921318657343978474607_<127>] SUBMIT/RESERVE

Status

Expression:	(55·10¹⁸⁸+53)/9
Composite Factor:	335382094382452262053791237276071923141765884201584329051391 003411894333744909123654454209371221320948468492131865734397 8474607 (127-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 190.44-digit and the GNFS difficulty is 126.53-digit. GNFS must be faster than SNFS. It will take about 4 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 61117_188.
Put the following polynomial file 61117_188.poly in there too.
And then, run "perl factMsieve.pl 61117_188".

61117_188.poly ^*1

# Murphy_E = 1.157454e-10, selected by Jeff Gilchrist
n: 3353820943824522620537912372760719231417658842015843290513910034118943337449091236544542093712213209484684921318657343978474607
Y0: -2625548429413531077760474
Y1: 60286404966257
c0: 68081307298291923989745076069399
c1: 5356871208883519836365291570
c2: -13099698895852305524151
c3: -28014524541481834
c4: 28144621888
c5: 26880
skew: 629762.92
type: gnfs
# selected mechanically
rlim: 7900000
alim: 7900000
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 127-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 35-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
35	1e6	118	Makoto Kamada	May 7, 2009
35	1e6	118 / 0
40	3e6	500	Erik Branger	May 10, 2009
		500 / 2318
		/ 1818
45	11e6	0 / 4365 (527)
45	11e6	/ 4365 (527)
50	43e6	0 / 7534 (1244)
50	43e6	/ 7534 (1244)
55	11e7	0 / 17765 (3125)
55	11e7	/ 17765 (3125)

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

echo 3353820943824522620537912372760719231417658842015843290513910034118943337449091236544542093712213209484684921318657343978474607 | ecm -n -c 1818 3e6

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

echo 3353820943824522620537912372760719231417658842015843290513910034118943337449091236544542093712213209484684921318657343978474607 | ecm -n -c 4365 11e6

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

echo 3353820943824522620537912372760719231417658842015843290513910034118943337449091236544542093712213209484684921318657343978474607 | ecm -n -c 7534 43e6

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

echo 3353820943824522620537912372760719231417658842015843290513910034118943337449091236544542093712213209484684921318657343978474607 | ecm -n -c 17765 11e7

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