Contribution and Reservation

(43·10²²⁶-7)/9 =: 4(7)₂₂₆_<227>; = 19 · [2514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883_<226>] RESERVED

Status

Expression:	(43·10²²⁶-7)/9
Composite Factor:	251461988304093567251461988304093567251461988304093567251461 988304093567251461988304093567251461988304093567251461988304 093567251461988304093567251461988304093567251461988304093567 2514619883040935672514619883040935672514619883 (226-digit)
Status:	Not factored. Reserved by Michael Dressner 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 229.63-digit and the GNFS difficulty is 225.40-digit. SNFS must be faster than GNFS. It will take about 188 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 47777_226.
Put the following polynomial file 47777_226.poly in there too.
And then, run "perl factMsieve.pl 47777_226".

47777_226.poly ^*1

n: 2514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883
m: 100000000000000000000000000000000000000
deg: 6
c6: 43
c0: -700
skew: 1.59
type: snfs
lss: 1
rlim: 47000000
alim: 47000000
lpbr: 30
lpba: 30
mfbr: 59
mfba: 59
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 226-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 35-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
35	1e6	0 / 0
40	3e6	800	Serge Batalov	Jan 29, 2009
		800 / 1266
		/ 466
45	11e6	310	Serge Batalov	Jan 29, 2009
		310 / 4302 (446)
		/ 3992 (136)
50	43e6	0 / 7454 (1138)
50	43e6	/ 7454 (1138)
55	11e7	0 / 17744 (3092)
55	11e7	/ 17744 (3092)

Command line to find prime factors up to about 40-digit

echo 2514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883 | ecm -n -c 466 3e6

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

echo 2514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883 | ecm -n -c 3992 11e6

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

echo 2514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883 | ecm -n -c 7454 43e6

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

echo 2514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883 | ecm -n -c 17744 11e7

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