Contribution and Reservation

(14·10¹⁹⁷-23)/9 =: 1(5)₁₉₆3_<198>; = 3 · 43 · 3571356734592851_<16> · 8160764602194575029_<19> · 376501481719133389972453446383_<30> · [109891738093046325077322651135173252077103201484245078671008609110972785624963035514012070014075186034316627804214647165243254054401_<132>] (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=3518916396 for P30 / Mar 18, 2008) SUBMIT/RESERVE

Status

Expression:	(14·10¹⁹⁷-23)/9
Composite Factor:	109891738093046325077322651135173252077103201484245078671008 609110972785624963035514012070014075186034316627804214647165 243254054401 (132-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 198.75-digit and the GNFS difficulty is 131.04-digit. GNFS must be faster than SNFS. It will take about 7 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 15553_197.
Put the following polynomial file 15553_197.poly in there too.
And then, run "perl factMsieve.pl 15553_197".

15553_197.poly ^*1

# Murphy_E = 6.400633e-11, selected by Jeff Gilchrist
n: 109891738093046325077322651135173252077103201484245078671008609110972785624963035514012070014075186034316627804214647165243254054401
Y0: -19576534341799516229397428
Y1: 273580858241237
c0: 15275129491140120257334836888445
c1: -767381195893339816113809552
c2: 4967635633760400958677
c3: 88731202901061528
c4: -29555707958
c5: 38220
skew: 213629.78
type: gnfs
# selected mechanically
rlim: 10400000
alim: 10400000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
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 132-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	2111	Wataru Sakai	Jul 14, 2009
40	3e6	2111 / 2111
45	11e6	0 / 3974
45	11e6	/ 3974
50	43e6	0 / 7469 (1133)
50	43e6	/ 7469 (1133)
55	11e7	0 / 17752 (3098)
55	11e7	/ 17752 (3098)
60	26e7	0 / 42014 (7636)
60	26e7	/ 42014 (7636)

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

echo 109891738093046325077322651135173252077103201484245078671008609110972785624963035514012070014075186034316627804214647165243254054401 | ecm -n -c 3974 11e6

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

echo 109891738093046325077322651135173252077103201484245078671008609110972785624963035514012070014075186034316627804214647165243254054401 | ecm -n -c 7469 43e6

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

echo 109891738093046325077322651135173252077103201484245078671008609110972785624963035514012070014075186034316627804214647165243254054401 | ecm -n -c 17752 11e7

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

echo 109891738093046325077322651135173252077103201484245078671008609110972785624963035514012070014075186034316627804214647165243254054401 | 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