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=====BACKGROUND=====

To better explain this, we gotta first ask ourselves the question: What is a prime number? How do we calculate prime numbers? What does a "prime" number mean?

A prime number is a natural number greater than 1 that is the product between the number itself times one. 
For example, the number 11 is a prime number because you can only obtain it by multiplying 11 X 1 = 11. 

However, since multiplication is commutative, it doesn't matter how you arrange the numbers the product will be the same, therefore the **factor pair** is one and the same:\\
  * 1 x 11 = 11 
  * 11 x 1 = 11

The property of a number being prime is called **primality**.

Taking this property into consideration, if there are prime numbers that are the product between **__ONE PAIR__** of factors, then there could be //"secondary"// numbers that are the product of __**TWO**__ separate **__pairs__** of factors. Therefore there could be "third-ary", a "fourth-ary", "fifth-ary" and so on to the "N-ary" __factor pairs__.

Example:
  * 11 x 1 = 1
  * 14 x 1 = 14, 7 x 2 = 14
  * 12 x 1 = 12, 6 x 2 = 12, 4 x 3 = 12
 

----

=== Computing N values ===

The n-ary value of something is determined by the number of "factor pairs" it possesses. For those who may have forgotten, a number's factors are the lesser numbers that multiply together to equal the number. For example, 2 has 1 factor pair, namely (1,2). Therefore, 2 has a n-ary value of 1 (or is a prime number). 4 would have two factor pairs, being (1,2 and 2,4). Thus an n-ary value of 2.
=====ALGORITHM: trial by division=====
Somewhere in the algorithm you may need to make use of the modulo (%) operator. The modulo operator gives you the remainder after a division. For example 5 % 2 would give you 1, since there is a remainder of 1 after dividing 5 by 2. This operator can be used to check if the result of two numbers being divided is a whole number (divider % divisor == 0).
=====SPECIFICATIONS=====

It is our task to build a program that will calculate and display **factor pairs** from an **n-ary** number.
This program will be timed and we will compare this program's computational time to future project's computational time in order to get a better understanding of the algorithms we use.
The computational time of the program should start prior to your algorithm and end after. Furthermore, the computational time of your program should be output to stderr while the computed values are output to stdout.





*Our task is to ask questions on Discord or in class and document our findings on this wiki page collaboratively, regarding the functionality of this project.

*For anybody interested in editing the wiki page, here is the dokuwiki user guide: [[https://www.dokuwiki.org/wiki:syntax#basic_text_formatting]] -Ash
=====PROGRAM=====

Once you've grabbed the cnv0 project directory, with the **grabit** command, you will have a skeleton source code file. This source code contains structs, functions, and a fprintf statement that will calculate how long it takes for your program to finish processing. This is only for timekeeping and referencing, it will not be used to calculate data in our algorithms. //(gotta confirm with Matt if this information is correct)//*

**Note:** If you are coding this project in c++ you should modify the Makefile that way make can still build the project. To do this go to the top of the make file and change CC=gcc to CC=g++, as well as removing the flag —-std=gnu18 two lines above.

The cnv0 program will accept 4 arguments, two are mandatory and two are optional.

<cli> 
lab46:~/src/SEMESTER/DESIG/PROJECT$ ./cnv0 qty nary [start] [end]
</cli>

<cli>
 ./cnv0     qty    nary  [start]   [end]
argv[0] argv[1] argv[2]  argv[3] argv[4]
</cli>

The first two arguments are mandatory, qty and nary.

The qty argument stands for quantity, this argument indicates how many **n-ary** will be displayed to output, from all the n-ary numbers available. 
example: If the program is looking for "second-ary" numbers, display only a quantity of 3 n-ary numbers. 
Therefore: 4 is second-ary, 10 is second-ary, and 14 is second-ary. (only display 3)

The nary argument stands for the n-ary degree, this argument indicates how many factor pairs a number is expected to have. 1 for n-ary is a prime number, with one factor pair, 10 for n-ary is a "tenth-ary" number with 10 factor pairs, etc. 

The two last arguments are optional, start and end.

The start argument is the lower bound of where the program will begin to check for n-ary numbers.

The end argument is the upper bound of where the program will stop checking for n-ary values.

Hence, if you have the following case:
<cli> 
lab46:~/src/SEMESTER/DESIG/PROJECT$ ./cnv0 5 1 7 20
7 11 13 17 19
</cli>

What these arguments are indicating is display 5 numbers, that are prime, start from seven, and stop at 20.

The program is to display timing information as well, with the core computation part of this project between the starting and stopping of the timer. This functionality is already included in the cnv0.c you grabbed.

=====OUTPUT SPECIFICATIONS=====
Output should be a space separated list of matching n-ary values with a newline at the end. Beneath that should be the amount of time it took for your script to complete. This doesn't matter for this project but in the next iteration, cnv1, we will be looking at the time and optimizing the amount of time it takes for the script to complete. The time it takes should be already included in your cnv0.c file, just make sure that your values have a newline at the end of the output.
=====VERIFICATION=====
There is no verify file so in order to verify that your script is working correctly, you can do this manually. To do so, you can enter values into your script, figure out what the output should be, and see if your script outputs that. If it doesn't match, check if either your script doesn't work correctly, or if you did your math wrong. You can also use the example below and compare your output.

<cli>
lab46:~/src/SEMESTER/DESIG/PROJECT$ ./cnv0 7 1 0 16
1 2 3 5 7 11 13
  x.xxxx (Time)
</cli>

<cli>
lab46:~/src/SEMESTER/DESIG/PROJECT$ ./cnv0 7 2 0 16
4 6 8 9 10 14 15
  x.xxxx (Time)
</cli>

<cli>
lab46:~/src/SEMESTER/DESIG/PROJECT$ ./cnv0 7 3 0 16
12 16
  x.xxxx (Time)
</cli>
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