Contribution and Reservation

(31·10¹⁹⁸+23)/9 =: 3(4)₁₉₇7_<199>; = 3 · 257 · 283 · [15786227992852403351365279566459256000167028476827599622556381022509633418324347914206433957296725579851069669716464068253539043161075031941650027473129039173779380843768793886350361581006010479_<194>] SUBMIT/RESERVE

Status

Expression:	(31·10¹⁹⁸+23)/9
Composite Factor:	157862279928524033513652795664592560001670284768275996225563 810225096334183243479142064339572967255798510696697164640682 535390431610750319416500274731290391737793808437687938863503 61581006010479 (194-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 200.89-digit and the GNFS difficulty is 193.20-digit. SNFS must be faster than GNFS. It will take about 21 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 34447_198.
Put the following polynomial file 34447_198.poly in there too.
And then, run "perl factMsieve.pl 34447_198".

34447_198.poly ^*1

n: 15786227992852403351365279566459256000167028476827599622556381022509633418324347914206433957296725579851069669716464068253539043161075031941650027473129039173779380843768793886350361581006010479
m: 5000000000000000000000000000000000000000
deg: 5
c5: 248
c0: 575
skew: 1.18
type: snfs
lss: 1
rlim: 15600000
alim: 15600000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6

*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 194-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	825	Wataru Sakai	Aug 14, 2009
35	1e6	825 / 825
40	3e6	0 / 2111
40	3e6	/ 2111
45	11e6	0 / 4441 (612)
45	11e6	/ 4441 (612)
50	43e6	0 / 7548 (1266)
50	43e6	/ 7548 (1266)
55	11e7	0 / 17769 (3131)
55	11e7	/ 17769 (3131)

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

echo 15786227992852403351365279566459256000167028476827599622556381022509633418324347914206433957296725579851069669716464068253539043161075031941650027473129039173779380843768793886350361581006010479 | ecm -n -c 2111 3e6

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

echo 15786227992852403351365279566459256000167028476827599622556381022509633418324347914206433957296725579851069669716464068253539043161075031941650027473129039173779380843768793886350361581006010479 | ecm -n -c 4441 11e6

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

echo 15786227992852403351365279566459256000167028476827599622556381022509633418324347914206433957296725579851069669716464068253539043161075031941650027473129039173779380843768793886350361581006010479 | ecm -n -c 7548 43e6

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

echo 15786227992852403351365279566459256000167028476827599622556381022509633418324347914206433957296725579851069669716464068253539043161075031941650027473129039173779380843768793886350361581006010479 | ecm -n -c 17769 11e7

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