Contribution and Reservation

(4·10¹⁹⁸-31)/9 =: (4)₁₉₇1_<198>; = 3 · 17167 · 543203 · [15886918229761599192394694978644128269021360775911427739021428070156555614521731193396400267232966641474462294196147851262571135263725121810907731554378074559914271722311543693376715630847_<188>] SUBMIT/RESERVE

Status

Expression:	(4·10¹⁹⁸-31)/9
Composite Factor:	158869182297615991923946949786441282690213607759114277390214 280701565556145217311933964002672329666414744622941961478512 625711352637251218109077315543780745599142717223115436933767 15630847 (188-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 198.60-digit and the GNFS difficulty is 187.20-digit. SNFS must be faster than GNFS. It will take about 17 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 44441_198.
Put the following polynomial file 44441_198.poly in there too.
And then, run "perl factMsieve.pl 44441_198".

44441_198.poly ^*1

n: 15886918229761599192394694978644128269021360775911427739021428070156555614521731193396400267232966641474462294196147851262571135263725121810907731554378074559914271722311543693376715630847
m: 2000000000000000000000000000000000000000
deg: 5
c5: 125
c0: -31
skew: 0.76
type: snfs
lss: 1
rlim: 14300000
alim: 14300000
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 188-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 25-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
25	5e4	250	Lionel Debroux	Oct 19, 2009
25	5e4	250 / 194
30	25e4	0 / 397
30	25e4	/ 397
35	1e6	0 / 901 (109)
35	1e6	/ 901 (109)
40	3e6	0 / 2350 (321)
40	3e6	/ 2350 (321)
45	11e6	0 / 4480 (681)
45	11e6	/ 4480 (681)

Command line to find prime factors up to about 30-digit

echo 15886918229761599192394694978644128269021360775911427739021428070156555614521731193396400267232966641474462294196147851262571135263725121810907731554378074559914271722311543693376715630847 | ecm -n -c 397 25e4

Command line to find prime factors up to about 35-digit

echo 15886918229761599192394694978644128269021360775911427739021428070156555614521731193396400267232966641474462294196147851262571135263725121810907731554378074559914271722311543693376715630847 | ecm -n -c 901 1e6

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

echo 15886918229761599192394694978644128269021360775911427739021428070156555614521731193396400267232966641474462294196147851262571135263725121810907731554378074559914271722311543693376715630847 | ecm -n -c 2350 3e6

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

echo 15886918229761599192394694978644128269021360775911427739021428070156555614521731193396400267232966641474462294196147851262571135263725121810907731554378074559914271722311543693376715630847 | ecm -n -c 4480 11e6

Submit factors

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