Contribution and Reservation

(23·10¹⁹⁴+1)/3 =: 7(6)₁₉₃7_<195>; = 13 · 139 · 78459255911_<11> · 234102535388474561689151_<24> · 28755254470177769678351594744207_<32> · [803305815778793560119943241710039446370201891384089344299540163842961294333911367771016525950573017814190338673989871897500803_<126>] (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=3024431625 for P32 / Aug 2, 2008) SUBMIT/RESERVE

Status

Expression:	(23·10¹⁹⁴+1)/3
Composite Factor:	803305815778793560119943241710039446370201891384089344299540 163842961294333911367771016525950573017814190338673989871897 500803 (126-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 196.36-digit and the GNFS difficulty is 125.90-digit. GNFS must be faster than SNFS. It will take about 4 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 76667_194.
Put the following polynomial file 76667_194.poly in there too.
And then, run "perl factMsieve.pl 76667_194".

76667_194.poly ^*1

# Murphy_E = 1.319630e-10, selected by Jeff Gilchrist
n: 803305815778793560119943241710039446370201891384089344299540163842961294333911367771016525950573017814190338673989871897500803
Y0: -1854130582467913736436627
Y1: 70052808396203
c0: -5872429247863459776045379108420
c1: -36947251314319403693743581
c2: 734013893611918337060
c3: -44532801047997
c4: -29348172097
c5: 36660
skew: 210297.4
type: gnfs
# selected mechanically
rlim: 7600000
alim: 7600000
lpbr: 27
lpba: 27
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5

*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 126-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	500	Erik Branger	Mar 17, 2009
		1604	Wataru Sakai	Aug 30, 2009
		2104 / 2104
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 803305815778793560119943241710039446370201891384089344299540163842961294333911367771016525950573017814190338673989871897500803 | ecm -n -c 3974 11e6

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

echo 803305815778793560119943241710039446370201891384089344299540163842961294333911367771016525950573017814190338673989871897500803 | ecm -n -c 7469 43e6

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

echo 803305815778793560119943241710039446370201891384089344299540163842961294333911367771016525950573017814190338673989871897500803 | ecm -n -c 17752 11e7

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

echo 803305815778793560119943241710039446370201891384089344299540163842961294333911367771016525950573017814190338673989871897500803 | 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