Contribution and Reservation

(43·10²⁴⁰-7)/9 =: 4(7)₂₄₀_<241>; = 337 · [14177382129904385097263435542367293109132871744147708539399934058687767886580942960764919221892515661061655126937026046818331684800527530497856907352456313880646224859874711506758984503791625453346521595779756017144741180349488954830201121_<239>] SUBMIT/RESERVE

Status

Expression:	(43·10²⁴⁰-7)/9
Composite Factor:	141773821299043850972634355423672931091328717441477085393999 340586877678865809429607649192218925156610616551269370260468 183316848005275304978569073524563138806462248598747115067589 84503791625453346521595779756017144741180349488954830201121 (239-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 241.63-digit and the GNFS difficulty is 238.15-digit. SNFS must be faster than GNFS. It will take about 472 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_240.
Put the following polynomial file 47777_240.poly in there too.
And then, run "perl factMsieve.pl 47777_240".

47777_240.poly ^*1

n: 14177382129904385097263435542367293109132871744147708539399934058687767886580942960764919221892515661061655126937026046818331684800527530497856907352456313880646224859874711506758984503791625453346521595779756017144741180349488954830201121
m: 10000000000000000000000000000000000000000
deg: 6
c6: 43
c0: -7
skew: 0.74
type: snfs
lss: 1
rlim: 75000000
alim: 75000000
lpbr: 30
lpba: 30
mfbr: 61
mfba: 61
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 239-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	810	Serge Batalov	Jan 29, 2009
		810 / 1253
		/ 443
45	11e6	314	Serge Batalov	Jan 29, 2009
		314 / 4300 (443)
		/ 3986 (129)
50	43e6	0 / 7452 (1137)
50	43e6	/ 7452 (1137)
55	11e7	0 / 17743 (3092)
55	11e7	/ 17743 (3092)

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

echo 14177382129904385097263435542367293109132871744147708539399934058687767886580942960764919221892515661061655126937026046818331684800527530497856907352456313880646224859874711506758984503791625453346521595779756017144741180349488954830201121 | ecm -n -c 443 3e6

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

echo 14177382129904385097263435542367293109132871744147708539399934058687767886580942960764919221892515661061655126937026046818331684800527530497856907352456313880646224859874711506758984503791625453346521595779756017144741180349488954830201121 | ecm -n -c 3986 11e6

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

echo 14177382129904385097263435542367293109132871744147708539399934058687767886580942960764919221892515661061655126937026046818331684800527530497856907352456313880646224859874711506758984503791625453346521595779756017144741180349488954830201121 | ecm -n -c 7452 43e6

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

echo 14177382129904385097263435542367293109132871744147708539399934058687767886580942960764919221892515661061655126937026046818331684800527530497856907352456313880646224859874711506758984503791625453346521595779756017144741180349488954830201121 | ecm -n -c 17743 11e7

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