Contribution and Reservation

(4·10²⁰⁰+23)/9 =: (4)₁₉₉7_<200>; = 978085421263_<12> · [45440248344621485907833599792184416681025187121498685779399108418427677320831843079956990499315249422498583430298688607358241505482195433421788060221494891913117768341927337009675717077169_<188>] SUBMIT/RESERVE

Status

Expression:	(4·10²⁰⁰+23)/9
Composite Factor:	454402483446214859078335997921844166810251871214986857793991 084184276773208318430799569904993152494224985834302986886073 582415054821954334217880602214948919131177683419273370096757 17077169 (188-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 200.60-digit and the GNFS difficulty is 187.66-digit. SNFS must be faster than GNFS. It will take about 20 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 44447_200.
Put the following polynomial file 44447_200.poly in there too.
And then, run "perl factMsieve.pl 44447_200".

44447_200.poly ^*1

n: 45440248344621485907833599792184416681025187121498685779399108418427677320831843079956990499315249422498583430298688607358241505482195433421788060221494891913117768341927337009675717077169
m: 10000000000000000000000000000000000000000
deg: 5
c5: 4
c0: 23
skew: 1.42
type: snfs
lss: 1
rlim: 15400000
alim: 15400000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6

*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 188-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	403	Luigi Morelli	Feb 19, 2009
30	25e4	403 / 403
35	1e6	0 / 828
35	1e6	/ 828
40	3e6	0 / 2337 (295)
40	3e6	/ 2337 (295)
45	11e6	0 / 4479 (678)
45	11e6	/ 4479 (678)
50	43e6	0 / 7553 (1277)
50	43e6	/ 7553 (1277)

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

echo 45440248344621485907833599792184416681025187121498685779399108418427677320831843079956990499315249422498583430298688607358241505482195433421788060221494891913117768341927337009675717077169 | ecm -n -c 828 1e6

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

echo 45440248344621485907833599792184416681025187121498685779399108418427677320831843079956990499315249422498583430298688607358241505482195433421788060221494891913117768341927337009675717077169 | ecm -n -c 2337 3e6

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

echo 45440248344621485907833599792184416681025187121498685779399108418427677320831843079956990499315249422498583430298688607358241505482195433421788060221494891913117768341927337009675717077169 | ecm -n -c 4479 11e6

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

echo 45440248344621485907833599792184416681025187121498685779399108418427677320831843079956990499315249422498583430298688607358241505482195433421788060221494891913117768341927337009675717077169 | ecm -n -c 7553 43e6

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