Contribution and Reservation

(10¹⁹⁶-7)/3 =: (3)₁₉₅1_<196>; = 109 · 11741231 · 633752989 · 28326817297_<11> · 527066786539_<12> · 67704288545514248426941515407_<29> · [4065734211912069651889418786821571190367441227208124424697089378343489919175810203932388911072813673779896556294261144324891921_<127>] (suberi / GMP-ECM 6.1.2 B1=11000000, sigma=2999796699 for P29 / Mar 4, 2007) SUBMIT/RESERVE

Status

Expression:	(10¹⁹⁶-7)/3
Composite Factor:	406573421191206965188941878682157119036744122720812442469708 937834348991917581020393238891107281367377989655629426114432 4891921 (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.

NFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 196.00-digit and the GNFS difficulty is 126.61-digit. GNFS must be faster than SNFS. It will take about 4 CPU-days to factor this composite number on 64-bit Opteron-2600MHz.

Steps of GNFS

Put factMsieve.pl to which $GGNFS_BIN_PATH and $NUM_CPUS were modified properly in the working directory 33331_196.
Put the following polynomial file 33331_196.poly in there too.
And then, run "perl factMsieve.pl 33331_196".

33331_196.poly

# Murphy_E = 1.180145e-10, selected by Jeff Gilchrist
n: 4065734211912069651889418786821571190367441227208124424697089378343489919175810203932388911072813673779896556294261144324891921
Y0: -2735989085765834116170955
Y1: 61865141112103
c0: -54921674240889182763440062713728
c1: 1128196434846411834828845240
c2: 3564748946151397425370
c3: -9872558320291725
c4: -17117218002
c5: 26520
skew: 438177.99
type: gnfs
# selected mechanically
rlim: 7900000
alim: 7900000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5

These parameters were not fully adjusted. The approximate expressions which were used for making the parameters are: d=log10(n); time=5*10^(d/20-5)[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 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	Mar 17, 2009
		1836	Wataru Sakai	Dec 6, 2009
		2336 / 2336
45	11e6	0 / 3962
45	11e6	/ 3962
50	43e6	0 / 7465 (1130)
50	43e6	/ 7465 (1130)
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 4065734211912069651889418786821571190367441227208124424697089378343489919175810203932388911072813673779896556294261144324891921 | ecm -n -c 3962 11e6

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

echo 4065734211912069651889418786821571190367441227208124424697089378343489919175810203932388911072813673779896556294261144324891921 | ecm -n -c 7465 43e6

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

echo 4065734211912069651889418786821571190367441227208124424697089378343489919175810203932388911072813673779896556294261144324891921 | ecm -n -c 17751 11e7

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

echo 4065734211912069651889418786821571190367441227208124424697089378343489919175810203932388911072813673779896556294261144324891921 | ecm -n -c 42014 26e7

Contribution and Reservation

Status

How to factor it

ECM, P-1, P+1

NFS

Steps of GNFS

See also

Efforts by ECM

Submit polynomial for GNFS

Submit factors

Make reservation