Contribution and Reservation

(16·10¹⁹⁹+17)/3 =: 5(3)₁₉₈9_<200>; = 157 · 281 · 372817 · [3242627400358107343317592694364536490571604930179523175530714235469759669721660830886118532996978665483648697917707236565977873564665570521482739433741161039793270390392516619153522502866751_<190>] SUBMIT/RESERVE

Status

Expression:	(16·10¹⁹⁹+17)/3
Composite Factor:	324262740035810734331759269436453649057160493017952317553071 423546975966972166083088611853299697866548364869791770723656 597787356466557052148273943374116103979327039039251661915352 2502866751 (190-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 200.90-digit and the GNFS difficulty is 189.51-digit. SNFS must be faster than GNFS. It will take about 21 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 53339_199.
Put the following polynomial file 53339_199.poly in there too.
And then, run "perl factMsieve.pl 53339_199".

53339_199.poly ^*1

n: 3242627400358107343317592694364536490571604930179523175530714235469759669721660830886118532996978665483648697917707236565977873564665570521482739433741161039793270390392516619153522502866751
m: 10000000000000000000000000000000000000000
deg: 5
c5: 8
c0: 85
skew: 1.60
type: snfs
lss: 1
rlim: 15600000
alim: 15600000
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 190-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	Mar 19, 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 3242627400358107343317592694364536490571604930179523175530714235469759669721660830886118532996978665483648697917707236565977873564665570521482739433741161039793270390392516619153522502866751 | ecm -n -c 786 1e6

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

echo 3242627400358107343317592694364536490571604930179523175530714235469759669721660830886118532996978665483648697917707236565977873564665570521482739433741161039793270390392516619153522502866751 | ecm -n -c 2318 3e6

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

echo 3242627400358107343317592694364536490571604930179523175530714235469759669721660830886118532996978665483648697917707236565977873564665570521482739433741161039793270390392516619153522502866751 | ecm -n -c 4475 11e6

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

echo 3242627400358107343317592694364536490571604930179523175530714235469759669721660830886118532996978665483648697917707236565977873564665570521482739433741161039793270390392516619153522502866751 | ecm -n -c 7553 43e6

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