Contribution and Reservation

(17·10¹⁹⁶+7)/3 =: 5(6)₁₉₅9_<197>; = 17923 · 33547 · 11733160988422813648861_<23> · 202389364004335365603661940527_<30> · [39688122813449770624655687326308901751486249521915691741113265342395973198339445933497456562808456736187201433958517028649860898911097567_<137>] (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=587039797 for P30 / Mar 29, 2009) SUBMIT/RESERVE

Status

Expression:	(17·10¹⁹⁶+7)/3
Composite Factor:	396881228134497706246556873263089017514862495219156917411132 653423959731983394459334974565628084567361872014339585170286 49860898911097567 (137-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 198.43-digit and the GNFS difficulty is 136.60-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 56669_196.
Put the following polynomial file 56669_196.poly in there too.
And then, run "perl factMsieve.pl 56669_196".

56669_196.poly ^*1

# Murphy_E = 3.063577e-11, selected by Jeff Gilchrist
n: 39688122813449770624655687326308901751486249521915691741113265342395973198339445933497456562808456736187201433958517028649860898911097567
Y0: -226852431271569028434599369
Y1: 1916311815167801
c0: 28821846926493683422802063708303616
c1: -49350240862111237430505784088
c2: -102751014820452440872222
c3: 31460216656638967
c4: 86393645082
c5: 66060
skew: 974354.11
type: gnfs
# selected mechanically
rlim: 14800000
alim: 14800000
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 40-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
40	3e6	2318	Wataru Sakai	Apr 25, 2009
40	3e6	2318 / 2318
45	11e6	0 / 3963
45	11e6	/ 3963
50	43e6	0 / 7465 (1130)
50	43e6	/ 7465 (1130)
55	11e7	0 / 17751 (3097)
55	11e7	/ 17751 (3097)
60	26e7	0 / 42014 (7636)
60	26e7	/ 42014 (7636)

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

echo 39688122813449770624655687326308901751486249521915691741113265342395973198339445933497456562808456736187201433958517028649860898911097567 | ecm -n -c 3963 11e6

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

echo 39688122813449770624655687326308901751486249521915691741113265342395973198339445933497456562808456736187201433958517028649860898911097567 | ecm -n -c 7465 43e6

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

echo 39688122813449770624655687326308901751486249521915691741113265342395973198339445933497456562808456736187201433958517028649860898911097567 | ecm -n -c 17751 11e7

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

echo 39688122813449770624655687326308901751486249521915691741113265342395973198339445933497456562808456736187201433958517028649860898911097567 | ecm -n -c 42014 26e7

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