Contribution and Reservation

(64·10²⁰⁵-1)/9 =: 7(1)₂₀₅_<206>; = 431 · 37940267 · 45453581976434362961_<20> · 3413498540067034957579963393050135213037_<40> · [28027991462592126727645456941213879374870484455341245911407229100340608719858666765731412775742675529856705668542399476690203589001246999_<137>] (Jo Yeong Uk / GMP-ECM 6.2.1 B1=3000000, sigma=27677106 for P40 / Jan 3, 2009) RESERVED

Status

Expression:	(64·10²⁰⁵-1)/9
Composite Factor:	280279914625921267276454569412138793748704844553412459114072 291003406087198586667657314127757426755298567056685423994766 90203589001246999 (137-digit)
Status:	Not factored. Reserved by Erik Branger 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 206.81-digit and the GNFS difficulty is 136.45-digit. GNFS must be faster than SNFS. It will take about 13 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 71111_205.
Put the following polynomial file 71111_205.poly in there too.
And then, run "perl factMsieve.pl 71111_205".

71111_205.poly ^*1

# Murphy_E = 3.341821e-11, selected by Jeff Gilchrist
n: 28027991462592126727645456941213879374870484455341245911407229100340608719858666765731412775742675529856705668542399476690203589001246999
Y0: -200712814366335223924707637
Y1: 1865037990862081
c0: 42756225136356909361925341794202800
c1: 271117863504155830697150367460
c2: -599164415210628480558292
c3: -255405301427474975
c4: 342673420962
c5: 86040
skew: 1286946.34
type: gnfs
# selected mechanically
rlim: 14600000
alim: 14600000
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 137-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 45-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
45	11e6	40	Serge Batalov	Dec 3, 2008
		2600	Jo Yeong Uk	Jan 29, 2009
		900	Jo Yeong Uk	Apr 2, 2009
		600	Erik Branger	Nov 19, 2009
		4140 / 3993
50	43e6	0 / 6541
50	43e6	/ 6541
55	11e7	0 / 17493 (2714)
55	11e7	/ 17493 (2714)
60	26e7	0 / 41949 (7525)
60	26e7	/ 41949 (7525)
65	85e7	0 / 69397 (13589)
65	85e7	/ 69397 (13589)

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

echo 28027991462592126727645456941213879374870484455341245911407229100340608719858666765731412775742675529856705668542399476690203589001246999 | ecm -n -c 6541 43e6

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

echo 28027991462592126727645456941213879374870484455341245911407229100340608719858666765731412775742675529856705668542399476690203589001246999 | ecm -n -c 17493 11e7

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

echo 28027991462592126727645456941213879374870484455341245911407229100340608719858666765731412775742675529856705668542399476690203589001246999 | ecm -n -c 41949 26e7

Command line to find prime factors up to about 65-digit

echo 28027991462592126727645456941213879374870484455341245911407229100340608719858666765731412775742675529856705668542399476690203589001246999 | ecm -n -c 69397 85e7

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

Cancel reservation