Contribution and Reservation

(25·10¹⁸⁷-7)/9 =: 2(7)₁₈₇_<188>; = 3 · 17 · 60427 · 23266589 · 3220232927_<10> · 13190123133080210978819742846348167_<35> · [9120684547627610714215780906860265471154414377404081152110777681241679158987645184483414176125079900482114653960681389330828861501_<130>] (Makoto Kamada / GMP-ECM 5.0.3 B1=4000000, sigma=2471953682 for P35 / Mar 3, 2005) SUBMIT/RESERVE

Status

Expression:	(25·10¹⁸⁷-7)/9
Composite Factor:	912068454762761071421578090686026547115441437740408115211077 768124167915898764518448341417612507990048211465396068138933 0828861501 (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 189.10-digit and the GNFS difficulty is 129.96-digit. GNFS must 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 27777_187.
Put the following polynomial file 27777_187.poly in there too.
And then, run "perl factMsieve.pl 27777_187".

27777_187.poly ^*1

# Murphy_E = 7.438125e-11, selected by Jeff Gilchrist
n: 9120684547627610714215780906860265471154414377404081152110777681241679158987645184483414176125079900482114653960681389330828861501
Y0: -11697761061513598361483220
Y1: 229953770231911
c0: 49966897853100149417955765176591
c1: 905549717722177365061505373
c2: -542982439681856261329
c3: -27469872819030813
c4: 14551541738
c5: 41640
skew: 347542.2
type: gnfs
# selected mechanically
rlim: 9800000
alim: 9800000
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 27, 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 9120684547627610714215780906860265471154414377404081152110777681241679158987645184483414176125079900482114653960681389330828861501 | ecm -n -c 3961 11e6

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

echo 9120684547627610714215780906860265471154414377404081152110777681241679158987645184483414176125079900482114653960681389330828861501 | ecm -n -c 7465 43e6

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

echo 9120684547627610714215780906860265471154414377404081152110777681241679158987645184483414176125079900482114653960681389330828861501 | ecm -n -c 17751 11e7

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

echo 9120684547627610714215780906860265471154414377404081152110777681241679158987645184483414176125079900482114653960681389330828861501 | 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