# Project Planning Question: **Download Questions PDF**

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## Write a function that counts the number of primes in the range [1-N]. Write the test cases for this function?

## Answer:

This is what I came up with (C#):

PSEUDO:

-Craete a list of numbers uptill n number - n being int

parameter

-Pass this list into a function to check for primilaty for

the number and then print primes wile we count for primes

BACKGROUND OF THIS SOLUTION:

THEORY:

- we know primes are the numbers starting from 2 are

divisible with 1 and themselves only i.e. n being a prime

number can only be divisble as n/n or n/1. testing from a

prime is called "primilatiy test" for a number...

-the simplest primality test is to see if given a number n

is divisible by an integer m from 2 to n-1. If n is

divisible by n then n is a composite number otherwise its a

prime...

TO SPEED UP THE COMPUTING WE CAN ALSO:

Rather than testing till n-1 we can test the number till

Square Root of n i.e. if n is a prime number it can always

be factored into 2 values.

REFERENCE:

See here if you want to be a mathematician ;-).

http://en.wikipedia.org/wiki/Primality_test

THE CODE:

I would assume you know how to deal with lists in c# so I

will not get into that. Just create an integer based items

list "list<int>" etc. in C# which adds digits to the list

till number n. HINT: use a for loop ...LOL!!

public void CountPrimes(list<int> c)

{

list<int> primes = c.FindAll(

delegate(int a)

for (int i = 2; i <= Math.Sqrt(a); i++)

{

if (a % i == 0)

return false; //is not a prime

return true;//is a prime

}

//list primes in a list box and get the total count

label1.Text = "Total Primes = " + Convert.ToString

(p.count);

for (int count = 2; count < p.count; count++)

{

listbox.Items.Add(Convert.ToString(p[i]));

}

}

PSEUDO:

-Craete a list of numbers uptill n number - n being int

parameter

-Pass this list into a function to check for primilaty for

the number and then print primes wile we count for primes

BACKGROUND OF THIS SOLUTION:

THEORY:

- we know primes are the numbers starting from 2 are

divisible with 1 and themselves only i.e. n being a prime

number can only be divisble as n/n or n/1. testing from a

prime is called "primilatiy test" for a number...

-the simplest primality test is to see if given a number n

is divisible by an integer m from 2 to n-1. If n is

divisible by n then n is a composite number otherwise its a

prime...

TO SPEED UP THE COMPUTING WE CAN ALSO:

Rather than testing till n-1 we can test the number till

Square Root of n i.e. if n is a prime number it can always

be factored into 2 values.

REFERENCE:

See here if you want to be a mathematician ;-).

http://en.wikipedia.org/wiki/Primality_test

THE CODE:

I would assume you know how to deal with lists in c# so I

will not get into that. Just create an integer based items

list "list<int>" etc. in C# which adds digits to the list

till number n. HINT: use a for loop ...LOL!!

public void CountPrimes(list<int> c)

{

list<int> primes = c.FindAll(

delegate(int a)

for (int i = 2; i <= Math.Sqrt(a); i++)

{

if (a % i == 0)

return false; //is not a prime

return true;//is a prime

}

//list primes in a list box and get the total count

label1.Text = "Total Primes = " + Convert.ToString

(p.count);

for (int count = 2; count < p.count; count++)

{

listbox.Items.Add(Convert.ToString(p[i]));

}

}

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