Contribution and Reservation

(34·10¹⁹⁷-61)/9 =: 3(7)₁₉₆1_<198>; = 53 · 2609 · [2732036258942396622560351886270151780684985773322951595549352226167603996165506756566730387394706117270245794873896438147904407658379757861233450087706399312812526868371296584231490253460646223_<193>] SUBMIT/RESERVE

Status

Expression:	(34·10¹⁹⁷-61)/9
Composite Factor:	273203625894239662256035188627015178068498577332295159554935 222616760399616550675656673038739470611727024579487389643814 790440765837975786123345008770639931281252686837129658423149 0253460646223 (193-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.

SNFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 199.13-digit and the GNFS difficulty is 192.44-digit. SNFS must be faster than GNFS. It will take about 18 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 37771_197.
Put the following polynomial file 37771_197.poly in there too.
And then, run "perl factMsieve.pl 37771_197".

37771_197.poly ^*1

n: 2732036258942396622560351886270151780684985773322951595549352226167603996165506756566730387394706117270245794873896438147904407658379757861233450087706399312812526868371296584231490253460646223
m: 2000000000000000000000000000000000000000
deg: 5
c5: 425
c0: -244
skew: 0.89
type: snfs
lss: 1
rlim: 14600000
alim: 14600000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5

*1 These parameters were not fully adjusted. The approximate expressions which were used for making the parameters are: deg=expt<=105?4:expt<=210?5:6 or expt<=144?4:6; d=log10(c[deg])+deg*log10(m)[digits]; time=10^(d/30-4)[hours]; skew=|c0/c[deg]|^(1/deg); rlim=round(7*10^(d/60+3)); lpbr=floor(d/25+21); mfbr=floor(d/8+31); rlambda=floor(d/25+18)/10;

Efforts by ECM

The efforts by ECM to find small factors of this 193-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	900	Lionel Debroux	Sep 24, 2009
35	1e6	900 / 825
40	3e6	0 / 2091
40	3e6	/ 2091
45	11e6	0 / 4437 (606)
45	11e6	/ 4437 (606)
50	43e6	0 / 7548 (1265)
50	43e6	/ 7548 (1265)
55	11e7	0 / 17769 (3131)
55	11e7	/ 17769 (3131)

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

echo 2732036258942396622560351886270151780684985773322951595549352226167603996165506756566730387394706117270245794873896438147904407658379757861233450087706399312812526868371296584231490253460646223 | ecm -n -c 2091 3e6

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

echo 2732036258942396622560351886270151780684985773322951595549352226167603996165506756566730387394706117270245794873896438147904407658379757861233450087706399312812526868371296584231490253460646223 | ecm -n -c 4437 11e6

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

echo 2732036258942396622560351886270151780684985773322951595549352226167603996165506756566730387394706117270245794873896438147904407658379757861233450087706399312812526868371296584231490253460646223 | ecm -n -c 7548 43e6

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

echo 2732036258942396622560351886270151780684985773322951595549352226167603996165506756566730387394706117270245794873896438147904407658379757861233450087706399312812526868371296584231490253460646223 | ecm -n -c 17769 11e7

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