Contribution and Reservation

(7·10²²⁶-43)/9 =: (7)₂₂₅3_<226>; = 3 · 67 · 73² · 359 · 960383 · [21060798860106230025410960143695469193574556541043669392384513582941842509179315024420164763674640561794834406649563646816128346586139621322103849651872165979633753645424948985574374495198866259398395930914117821_<212>] SUBMIT/RESERVE

Status

Expression:	(7·10²²⁶-43)/9
Composite Factor:	210607988601062300254109601436954691935745565410436693923845 135829418425091793150244201647636746405617948344066495636468 161283465861396213221038496518721659796337536454249489855743 74495198866259398395930914117821 (212-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 228.24-digit and the GNFS difficulty is 211.32-digit. SNFS must be faster than GNFS. It will take about 169 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 77773_226.
Put the following polynomial file 77773_226.poly in there too.
And then, run "perl factMsieve.pl 77773_226".

77773_226.poly ^*1

n: 21060798860106230025410960143695469193574556541043669392384513582941842509179315024420164763674640561794834406649563646816128346586139621322103849651872165979633753645424948985574374495198866259398395930914117821
m: 50000000000000000000000000000000000000
deg: 6
c6: 112
c0: -1075
skew: 1.46
type: snfs
lss: 1
rlim: 45000000
alim: 45000000
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 212-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 30-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
30	25e4	0 / 0
35	1e6	118	Makoto Kamada	May 31, 2009
		118 / 904
		/ 786
40	3e6	0 / 2318 (280)
40	3e6	/ 2318 (280)
45	11e6	0 / 4475 (672)
45	11e6	/ 4475 (672)
50	43e6	0 / 7553 (1276)
50	43e6	/ 7553 (1276)

Command line to find prime factors up to about 35-digit

echo 21060798860106230025410960143695469193574556541043669392384513582941842509179315024420164763674640561794834406649563646816128346586139621322103849651872165979633753645424948985574374495198866259398395930914117821 | ecm -n -c 786 1e6

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

echo 21060798860106230025410960143695469193574556541043669392384513582941842509179315024420164763674640561794834406649563646816128346586139621322103849651872165979633753645424948985574374495198866259398395930914117821 | ecm -n -c 2318 3e6

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

echo 21060798860106230025410960143695469193574556541043669392384513582941842509179315024420164763674640561794834406649563646816128346586139621322103849651872165979633753645424948985574374495198866259398395930914117821 | ecm -n -c 4475 11e6

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

echo 21060798860106230025410960143695469193574556541043669392384513582941842509179315024420164763674640561794834406649563646816128346586139621322103849651872165979633753645424948985574374495198866259398395930914117821 | ecm -n -c 7553 43e6

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