Contribution and Reservation

(43·10²²⁷-7)/9 =: 4(7)₂₂₇_<228>; = 3³ · 17 · 281 · 60289285487_<11> · [61442206529043889798511661189828252117796614689695151690169043640612781510235094663334224008521698579298722982533969117848109527240874593665515163967943367406043132094367681131480561070284492018507488575950745349_<212>] SUBMIT/RESERVE

Status

Expression:	(43·10²²⁷-7)/9
Composite Factor:	614422065290438897985116611898282521177966146896951516901690 436406127815102350946633342240085216985792987229825339691178 481095272408745936655151639679433674060431320943676811314805 61070284492018507488575950745349 (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 229.63-digit and the GNFS difficulty is 211.79-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_227.
Put the following polynomial file 47777_227.poly in there too.
And then, run "perl factMsieve.pl 47777_227".

47777_227.poly ^*1

n: 61442206529043889798511661189828252117796614689695151690169043640612781510235094663334224008521698579298722982533969117848109527240874593665515163967943367406043132094367681131480561070284492018507488575950745349
m: 100000000000000000000000000000000000000
deg: 6
c6: 43
c0: -70
skew: 1.08
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 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	430	Makoto Kamada	Jan 27, 2009
30	25e4	430 / 430
35	1e6	0 / 825
35	1e6	/ 825
40	3e6	0 / 2336 (294)
40	3e6	/ 2336 (294)
45	11e6	0 / 4479 (677)
45	11e6	/ 4479 (677)
50	43e6	0 / 7553 (1277)
50	43e6	/ 7553 (1277)

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

echo 61442206529043889798511661189828252117796614689695151690169043640612781510235094663334224008521698579298722982533969117848109527240874593665515163967943367406043132094367681131480561070284492018507488575950745349 | ecm -n -c 825 1e6

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

echo 61442206529043889798511661189828252117796614689695151690169043640612781510235094663334224008521698579298722982533969117848109527240874593665515163967943367406043132094367681131480561070284492018507488575950745349 | ecm -n -c 2336 3e6

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

echo 61442206529043889798511661189828252117796614689695151690169043640612781510235094663334224008521698579298722982533969117848109527240874593665515163967943367406043132094367681131480561070284492018507488575950745349 | ecm -n -c 4479 11e6

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

echo 61442206529043889798511661189828252117796614689695151690169043640612781510235094663334224008521698579298722982533969117848109527240874593665515163967943367406043132094367681131480561070284492018507488575950745349 | ecm -n -c 7553 43e6

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