Contribution and Reservation

(16·10²¹³-61)/9 =: 1(7)₂₁₂1_<214>; = 7 · 11 · 36739 · 701735753995253_<15> · 9242562959716967_<16> · 15343317696192422017522869439279665157_<38> · [6315011082326212861759378001460381655744123914330053236853058428366793582916494518062439711742158493507181037630191574610156925315769334851_<139>] (suberi / GMP-ECM 6.1.2 B1=3000000, sigma=1376874633 for P38 / Apr 4, 2007) SUBMIT/RESERVE

Status

Expression:	(16·10²¹³-61)/9
Composite Factor:	631501108232621286175937800146038165574412391433005323685305 842836679358291649451806243971174215849350718103763019157461 0156925315769334851 (139-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 214.20-digit and the GNFS difficulty is 138.80-digit. GNFS must be faster than SNFS. It will take about 17 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 17771_213.
Put the following polynomial file 17771_213.poly in there too.
And then, run "perl factMsieve.pl 17771_213".

17771_213.poly ^*1

# Murphy_E = 2.239904e-11, selected by Jeff Gilchrist
n: 6315011082326212861759378001460381655744123914330053236853058428366793582916494518062439711742158493507181037630191574610156925315769334851
Y0: -545548548001369938857510366
Y1: 4181495085807679
c0: -2661762105578500314980441754934185
c1: 35406203595953285477099322953
c2: 32113352736010501838393
c3: -175753517887987380
c4: -79686497461
c5: 130680
skew: 685063.28
type: gnfs
# selected mechanically
rlim: 16900000
alim: 16900000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
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 139-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 45-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
45	11e6	3970	Wataru Sakai	Sep 30, 2009
45	11e6	3970 / 0
50	43e6	3000	Wataru Sakai	Oct 11, 2009
		3000 / 6576
		/ 3576
55	11e7	0 / 16433 (1484)
55	11e7	/ 16433 (1484)
60	26e7	0 / 41600 (7068)
60	26e7	/ 41600 (7068)
65	85e7	0 / 69325 (13476)
65	85e7	/ 69325 (13476)

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

echo 6315011082326212861759378001460381655744123914330053236853058428366793582916494518062439711742158493507181037630191574610156925315769334851 | ecm -n -c 3576 43e6

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

echo 6315011082326212861759378001460381655744123914330053236853058428366793582916494518062439711742158493507181037630191574610156925315769334851 | ecm -n -c 16433 11e7

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

echo 6315011082326212861759378001460381655744123914330053236853058428366793582916494518062439711742158493507181037630191574610156925315769334851 | ecm -n -c 41600 26e7

Command line to find prime factors up to about 65-digit

echo 6315011082326212861759378001460381655744123914330053236853058428366793582916494518062439711742158493507181037630191574610156925315769334851 | ecm -n -c 69325 85e7

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