Contribution and Reservation

(56·10²⁰²+61)/9 =: 6(2)₂₀₁9_<203>; = 3 · 1039 · 3727 · 229043621 · 10618429103_<11> · 1669230736042131981857_<22> · 50428565925821293620377267_<26> · [26162416726915977316434924783694215691323111701322415965626973690778855896787041219293447896744657569020451001529666599914969576823_<131>] SUBMIT/RESERVE

Status

Expression:	(56·10²⁰²+61)/9
Composite Factor:	261624167269159773164349247836942156913231117013224159656269 736907788558967870412192934478967446575690204510015296665999 14969576823 (131-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 203.75-digit and the GNFS difficulty is 130.42-digit. GNFS must be faster than SNFS. It will take about 7 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 62229_202.
Put the following polynomial file 62229_202.poly in there too.
And then, run "perl factMsieve.pl 62229_202".

62229_202.poly ^*1

# Murphy_E = 7.540377e-11, selected by Jeff Gilchrist
n: 26162416726915977316434924783694215691323111701322415965626973690778855896787041219293447896744657569020451001529666599914969576823
Y0: -14409151452125978942057496
Y1: 223845488142281
c0: -121325131323099180909652384477105
c1: 719965104559165303929902238
c2: 4852016030299408215477
c3: -58154120580746486
c4: -15821216796
c5: 42120
skew: 477174.33
type: gnfs
# selected mechanically
rlim: 10000000
alim: 10000000
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 131-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	2104	Wataru Sakai	Aug 27, 2009
40	3e6	2104 / 2104
45	11e6	0 / 3974
45	11e6	/ 3974
50	43e6	0 / 7469 (1133)
50	43e6	/ 7469 (1133)
55	11e7	0 / 17752 (3098)
55	11e7	/ 17752 (3098)
60	26e7	0 / 42014 (7636)
60	26e7	/ 42014 (7636)

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

echo 26162416726915977316434924783694215691323111701322415965626973690778855896787041219293447896744657569020451001529666599914969576823 | ecm -n -c 3974 11e6

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

echo 26162416726915977316434924783694215691323111701322415965626973690778855896787041219293447896744657569020451001529666599914969576823 | ecm -n -c 7469 43e6

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

echo 26162416726915977316434924783694215691323111701322415965626973690778855896787041219293447896744657569020451001529666599914969576823 | ecm -n -c 17752 11e7

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

echo 26162416726915977316434924783694215691323111701322415965626973690778855896787041219293447896744657569020451001529666599914969576823 | 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