Contribution and Reservation

10²³⁵-9 =: (9)₂₃₄1_<235>; = 1115363 · 5476400107084512893933_<22> · [1637150466542620463521641864646810936730159962508376375974999081043970766985055221845360455776234416343940654734610211656283611664347262318575325514391313947370826427676824204286688910344967227394380562903729_<208>] SUBMIT/RESERVE

Status

Expression:	10²³⁵-9
Composite Factor:	163715046654262046352164186464681093673015996250837637597499 908104397076698505522184536045577623441634394065473461021165 628361166434726231857532551439131394737082642767682420428668 8910344967227394380562903729 (208-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 235.00-digit and the GNFS difficulty is 207.21-digit. SNFS must be faster than GNFS. It will take about 284 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_235.
Put the following polynomial file 99991_235.poly in there too.
And then, run "perl factMsieve.pl 99991_235".

99991_235.poly ^*1

n: 1637150466542620463521641864646810936730159962508376375974999081043970766985055221845360455776234416343940654734610211656283611664347262318575325514391313947370826427676824204286688910344967227394380562903729
m: 1000000000000000000000000000000000000000
deg: 6
c6: 10
c0: -9
skew: 0.98
type: snfs
lss: 1
rlim: 58000000
alim: 58000000
lpbr: 30
lpba: 30
mfbr: 60
mfba: 60
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 208-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	759	Dmitry Domanov	Jun 30, 2009
		759 / 4479
		/ 3720
50	43e6	0 / 7383 (1061)
50	43e6	/ 7383 (1061)
55	11e7	0 / 17722 (3063)
55	11e7	/ 17722 (3063)
60	26e7	0 / 42005 (7623)
60	26e7	/ 42005 (7623)

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

echo 1637150466542620463521641864646810936730159962508376375974999081043970766985055221845360455776234416343940654734610211656283611664347262318575325514391313947370826427676824204286688910344967227394380562903729 | ecm -n -c 3720 11e6

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

echo 1637150466542620463521641864646810936730159962508376375974999081043970766985055221845360455776234416343940654734610211656283611664347262318575325514391313947370826427676824204286688910344967227394380562903729 | ecm -n -c 7383 43e6

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

echo 1637150466542620463521641864646810936730159962508376375974999081043970766985055221845360455776234416343940654734610211656283611664347262318575325514391313947370826427676824204286688910344967227394380562903729 | ecm -n -c 17722 11e7

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

echo 1637150466542620463521641864646810936730159962508376375974999081043970766985055221845360455776234416343940654734610211656283611664347262318575325514391313947370826427676824204286688910344967227394380562903729 | ecm -n -c 42005 26e7

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