Contribution and Reservation

10²⁴⁵-9 =: (9)₂₄₄1_<245>; = 40974399286914864833693_<23> · 5715411392874728022457273897097329_<34> · [427011831602112740817913621551742021102073286561629462464731021857158629869115131922752233372580108125425120862025257386114216115947550294412616236983597923505019820154999571664743031506003_<189>] (Dmitry Domanov / GMP-ECM 6.2.3 B1=11000000, sigma=1951669128 for P34 / May 11, 2009) SUBMIT/RESERVE

Status

Expression:	10²⁴⁵-9
Composite Factor:	427011831602112740817913621551742021102073286561629462464731 021857158629869115131922752233372580108125425120862025257386 114216115947550294412616236983597923505019820154999571664743 031506003 (189-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 245.70-digit and the GNFS difficulty is 188.63-digit. SNFS must be faster than GNFS. It will take about 645 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 99991_245.
Put the following polynomial file 99991_245.poly in there too.
And then, run "perl factMsieve.pl 99991_245".

99991_245.poly ^*1

n: 427011831602112740817913621551742021102073286561629462464731021857158629869115131922752233372580108125425120862025257386114216115947550294412616236983597923505019820154999571664743031506003
m: 50000000000000000000000000000000000000000
deg: 6
c6: 32
c0: -45
skew: 1.06
type: snfs
lss: 1
rlim: 87000000
alim: 87000000
lpbr: 30
lpba: 30
mfbr: 61
mfba: 61
rlambda: 2.7
alambda: 2.7

*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 189-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	0 / 0
45	11e6	600	Dmitry Domanov	May 11, 2009
		709	Dmitry Domanov	Jun 30, 2009
		1309 / 4479
		/ 3170
50	43e6	0 / 7260 (904)
50	43e6	/ 7260 (904)
55	11e7	0 / 17688 (3012)
55	11e7	/ 17688 (3012)
60	26e7	0 / 41997 (7608)
60	26e7	/ 41997 (7608)

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

echo 427011831602112740817913621551742021102073286561629462464731021857158629869115131922752233372580108125425120862025257386114216115947550294412616236983597923505019820154999571664743031506003 | ecm -n -c 3170 11e6

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

echo 427011831602112740817913621551742021102073286561629462464731021857158629869115131922752233372580108125425120862025257386114216115947550294412616236983597923505019820154999571664743031506003 | ecm -n -c 7260 43e6

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

echo 427011831602112740817913621551742021102073286561629462464731021857158629869115131922752233372580108125425120862025257386114216115947550294412616236983597923505019820154999571664743031506003 | ecm -n -c 17688 11e7

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

echo 427011831602112740817913621551742021102073286561629462464731021857158629869115131922752233372580108125425120862025257386114216115947550294412616236983597923505019820154999571664743031506003 | ecm -n -c 41997 26e7

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