Contribution and Reservation

(43·10²¹⁵-7)/9 =: 4(7)₂₁₅_<216>; = 3 · 3174593 · 38918513 · 821426563553833_<15> · 1736471325720577418783621_<25> · 409313660865770307266297021_<27> · [2207841030190554585460252072204964640229072917619531868383189745070442478968228423473154639071982225639380156579222713767206159126954467_<136>] SUBMIT/RESERVE

Status

Expression:	(43·10²¹⁵-7)/9
Composite Factor:	220784103019055458546025207220496464022907291761953186838318 974507044247896822842347315463907198222563938015657922271376 7206159126954467 (136-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 217.63-digit and the GNFS difficulty is 135.34-digit. GNFS must be faster than SNFS. It will take about 12 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 47777_215.
Put the following polynomial file 47777_215.poly in there too.
And then, run "perl factMsieve.pl 47777_215".

47777_215.poly ^*1

# Murphy_E = 3.764431e-11, selected by Jeff Gilchrist
n: 2207841030190554585460252072204964640229072917619531868383189745070442478968228423473154639071982225639380156579222713767206159126954467
Y0: -124262160057903236137264105
Y1: 1323277366671947
c0: 2841680698820019263896428682763856
c1: 6144454614164526235541628720
c2: -15087325150672164750400
c3: -97856575158651320
c4: 7415452329
c5: 74520
skew: 731103.49
type: gnfs
# selected mechanically
rlim: 13600000
alim: 13600000
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 136-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 35-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
35	1e6	0 / 0
40	3e6	900	Dmitry Domanov	May 7, 2009
		300	Dmitry Domanov	May 7, 2009
		1200 / 2336
		/ 1136
45	11e6	0 / 4214 (330)
45	11e6	/ 4214 (330)
50	43e6	0 / 7508 (1201)
50	43e6	/ 7508 (1201)
55	11e7	0 / 17760 (3115)
55	11e7	/ 17760 (3115)

Command line to find prime factors up to about 40-digit

echo 2207841030190554585460252072204964640229072917619531868383189745070442478968228423473154639071982225639380156579222713767206159126954467 | ecm -n -c 1136 3e6

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

echo 2207841030190554585460252072204964640229072917619531868383189745070442478968228423473154639071982225639380156579222713767206159126954467 | ecm -n -c 4214 11e6

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

echo 2207841030190554585460252072204964640229072917619531868383189745070442478968228423473154639071982225639380156579222713767206159126954467 | ecm -n -c 7508 43e6

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

echo 2207841030190554585460252072204964640229072917619531868383189745070442478968228423473154639071982225639380156579222713767206159126954467 | ecm -n -c 17760 11e7

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