Contribution and Reservation

(14·10¹⁹⁶-41)/9 =: 1(5)₁₉₅1_<197>; = 43 · 12991941439670998826484083573_<29> · 31549870079323557671928299889097_<32> · [882562440577446030345916906651940795515837407245481246517202735480841275954656517617252892526279545364367486770393761420751543094322497_<135>] (matsuix / GMP-ECM 6.0 B1=6700417, sigma=1028308536 for P29 / Nov 11, 2007) (Serge Batalov / GMP-ECM 6.2.1 B1=1000000, sigma=1933614541 for P32 / Jul 12, 2008) SUBMIT/RESERVE

Status

Expression:	(14·10¹⁹⁶-41)/9
Composite Factor:	882562440577446030345916906651940795515837407245481246517202 735480841275954656517617252892526279545364367486770393761420 751543094322497 (135-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 197.15-digit and the GNFS difficulty is 134.95-digit. GNFS must be faster than SNFS. It will take about 11 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 15551_196.
Put the following polynomial file 15551_196.poly in there too.
And then, run "perl factMsieve.pl 15551_196".

15551_196.poly ^*1

# Murphy_E = 3.569799e-11, selected by Jeff Gilchrist
n: 882562440577446030345916906651940795515837407245481246517202735480841275954656517617252892526279545364367486770393761420751543094322497
Y0: -104190313431655748740972775
Y1: 988063353355529
c0: 241836179370501773016612866930928
c1: 3329214294338094693480908414
c2: 2463253944760115275988
c3: -54389529948658861
c4: 11347927070
c5: 71880
skew: 420291.04
type: gnfs
# selected mechanically
rlim: 13300000
alim: 13300000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.6
alambda: 2.6

*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 135-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	Jan 31, 2009
		1850	Wataru Sakai	May 3, 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 882562440577446030345916906651940795515837407245481246517202735480841275954656517617252892526279545364367486770393761420751543094322497 | ecm -n -c 3961 11e6

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

echo 882562440577446030345916906651940795515837407245481246517202735480841275954656517617252892526279545364367486770393761420751543094322497 | ecm -n -c 7465 43e6

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

echo 882562440577446030345916906651940795515837407245481246517202735480841275954656517617252892526279545364367486770393761420751543094322497 | ecm -n -c 17751 11e7

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

echo 882562440577446030345916906651940795515837407245481246517202735480841275954656517617252892526279545364367486770393761420751543094322497 | 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