Contribution and Reservation

(4·10¹⁹⁸-13)/9 =: (4)₁₉₇3_<198>; = 523 · 82737301 · 22861189383523_<14> · 109004345405742704229513258503_<30> · [4121656653229606688891632821619209502441186611362878540444545066393408185585679257868260089902556418333145433375944552756831904252394732003086489_<145>] (Serge Batalov / GMP-ECM 6.2.1 B1=1000000, sigma=1727263834 for P30 / Jul 17, 2008) SUBMIT/RESERVE

Status

Expression:	(4·10¹⁹⁸-13)/9
Composite Factor:	412165665322960668889163282161920950244118661136287854044454 506639340818558567925786826008990255641833314543337594455275 6831904252394732003086489 (145-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 198.60-digit and the GNFS difficulty is 144.62-digit. SNFS must be faster than GNFS. It will take about 17 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 44443_198.
Put the following polynomial file 44443_198.poly in there too.
And then, run "perl factMsieve.pl 44443_198".

44443_198.poly ^*1

n: 4121656653229606688891632821619209502441186611362878540444545066393408185585679257868260089902556418333145433375944552756831904252394732003086489
m: 2000000000000000000000000000000000000000
deg: 5
c5: 125
c0: -13
skew: 0.64
type: snfs
lss: 1
rlim: 14300000
alim: 14300000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5

*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 145-digit composite number are not reported yet. Please report your efforts by ECM. (Anonymous reports are not acceptable)

Level	B1	Reported runs Total / Required runs (Required runs for lower level)
20	11e3	0 / 74
20	11e3	/ 74
25	5e4	0 / 214 (21)
25	5e4	/ 214 (21)
30	25e4	0 / 430 (50)
30	25e4	/ 430 (50)
35	1e6	0 / 904 (118)
35	1e6	/ 904 (118)
40	3e6	0 / 2350 (322)
40	3e6	/ 2350 (322)

Command line to find prime factors up to about 20-digit

echo 4121656653229606688891632821619209502441186611362878540444545066393408185585679257868260089902556418333145433375944552756831904252394732003086489 | ecm -n -c 74 11e3

Command line to find prime factors up to about 25-digit

echo 4121656653229606688891632821619209502441186611362878540444545066393408185585679257868260089902556418333145433375944552756831904252394732003086489 | ecm -n -c 214 5e4

Command line to find prime factors up to about 30-digit

echo 4121656653229606688891632821619209502441186611362878540444545066393408185585679257868260089902556418333145433375944552756831904252394732003086489 | ecm -n -c 430 25e4

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

echo 4121656653229606688891632821619209502441186611362878540444545066393408185585679257868260089902556418333145433375944552756831904252394732003086489 | ecm -n -c 904 1e6

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

echo 4121656653229606688891632821619209502441186611362878540444545066393408185585679257868260089902556418333145433375944552756831904252394732003086489 | ecm -n -c 2350 3e6

Submit factors

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