Contribution and Reservation

(28·10²⁰⁰-1)/9 =: 3(1)₂₀₀_<201>; = 1704023 · [182574478813438029364105479275286255591098894270271651914974804395897890527951272436528797505145829082771248457979212200252643955575195353062201103571437187826168491335569479467771920397266416657_<195>] SUBMIT/RESERVE

Status

Expression:	(28·10²⁰⁰-1)/9
Composite Factor:	182574478813438029364105479275286255591098894270271651914974 804395897890527951272436528797505145829082771248457979212200 252643955575195353062201103571437187826168491335569479467771 920397266416657 (195-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.

NFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 201.45-digit and the GNFS difficulty is 194.26-digit. SNFS must be faster than GNFS. It will take about 22 CPU-days to factor this composite number on 64-bit Opteron-2600MHz.

Steps of SNFS

Put factMsieve.pl to which $GGNFS_BIN_PATH and $NUM_CPUS were modified properly in the working directory 31111_200.
Put the following polynomial file 31111_200.poly in there too.
And then, run "perl factMsieve.pl 31111_200".

31111_200.poly

n: 182574478813438029364105479275286255591098894270271651914974804395897890527951272436528797505145829082771248457979212200252643955575195353062201103571437187826168491335569479467771920397266416657
m: 10000000000000000000000000000000000000000
deg: 5
c5: 28
c0: -1
skew: 0.51
type: snfs
lss: 1
rlim: 15900000
alim: 15900000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6

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 195-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	400	Serge Batalov	Nov 25, 2008
40	3e6	400 / 0
45	11e6	690	Dmitry Domanov	Jan 9, 2010
		690 / 4392
		/ 3702
50	43e6	0 / 7384 (1056)
50	43e6	/ 7384 (1056)
55	11e7	0 / 17723 (3063)
55	11e7	/ 17723 (3063)
60	26e7	0 / 42006 (7624)
60	26e7	/ 42006 (7624)

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

echo 182574478813438029364105479275286255591098894270271651914974804395897890527951272436528797505145829082771248457979212200252643955575195353062201103571437187826168491335569479467771920397266416657 | ecm -n -c 3702 11e6

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

echo 182574478813438029364105479275286255591098894270271651914974804395897890527951272436528797505145829082771248457979212200252643955575195353062201103571437187826168491335569479467771920397266416657 | ecm -n -c 7384 43e6

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

echo 182574478813438029364105479275286255591098894270271651914974804395897890527951272436528797505145829082771248457979212200252643955575195353062201103571437187826168491335569479467771920397266416657 | ecm -n -c 17723 11e7

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

echo 182574478813438029364105479275286255591098894270271651914974804395897890527951272436528797505145829082771248457979212200252643955575195353062201103571437187826168491335569479467771920397266416657 | ecm -n -c 42006 26e7

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