Contribution and Reservation

(28·10¹⁹⁰+53)/9 =: 3(1)₁₈₉7_<191>; = 37 · 5503 · 4344444898747_<13> · 373824672452742884881_<21> · 501430285359458032167749_<24> · [187629650365522389134314363137377857016569321584471988619377285921208654594896913763467687419071693765552811281606096693896348129_<129>] SUBMIT/RESERVE

Status

Expression:	(28·10¹⁹⁰+53)/9
Composite Factor:	187629650365522389134314363137377857016569321584471988619377 285921208654594896913763467687419071693765552811281606096693 896348129 (129-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 191.45-digit and the GNFS difficulty is 128.27-digit. GNFS must be faster than SNFS. It will take about 5 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 31117_190.
Put the following polynomial file 31117_190.poly in there too.
And then, run "perl factMsieve.pl 31117_190".

31117_190.poly ^*1

# Murphy_E = 9.617949e-11, selected by Jeff Gilchrist
n: 187629650365522389134314363137377857016569321584471988619377285921208654594896913763467687419071693765552811281606096693896348129
Y0: -5820800135888719148285029
Y1: 116561456646041
c0: -1952737910919195637279392526579200
c1: 14807086180600964619864314088
c2: 13315738832932324607923
c3: -66548770985141010
c4: -29289272256
c5: 28080
skew: 793179.35
type: gnfs
# selected mechanically
rlim: 8800000
alim: 8800000
lpbr: 28
lpba: 28
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 129-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
		1836	Wataru Sakai	Nov 27, 2009
		2336 / 2336
45	11e6	0 / 3962
45	11e6	/ 3962
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 187629650365522389134314363137377857016569321584471988619377285921208654594896913763467687419071693765552811281606096693896348129 | ecm -n -c 3962 11e6

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

echo 187629650365522389134314363137377857016569321584471988619377285921208654594896913763467687419071693765552811281606096693896348129 | ecm -n -c 7465 43e6

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

echo 187629650365522389134314363137377857016569321584471988619377285921208654594896913763467687419071693765552811281606096693896348129 | ecm -n -c 17751 11e7

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

echo 187629650365522389134314363137377857016569321584471988619377285921208654594896913763467687419071693765552811281606096693896348129 | 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