Problem 7 projecteuler.net Matlab 10001st prime

Problem

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.
What is the 10 001st prime number? Solve using Matlab?

Solution

Here we will use the isprime function built in matlab. The program is simple. the explanation is given below the program. 

Program

function j = nprime(n)
%This function will give the value of the nth prime number.

counter = 0;
i = 2;
while (counter < n)
    if (isprime(i) == logical(1))
        counter = counter+1;
        j = i;
    end
    i = i+1;
end

Get the matlab file of the above function from here: nprime.m

Explanation

Here we will use two variables counter and i. Counter is used to count the index or the place or the rank of the current prime number during iteration, when compared to the rank of 2(rank is 1 for 2), and i is used to iterate through the numbers from 2 to some unknown number(This is the nth prime number).

We can make it easy to understand by going through the iterations

First iteration

Before the first iteration, counter = 0 and i = 2;

During the iteration:

The condition for the if statement is satisfied ( i = 2 is a prime number)

Now thus the value of counter increased from 0 to 1 and a new variable is created to store the prime number whose value becomes 2, at the end of the if statement the value of the i increases from 2 to 3.

Second iteration

During the second iteration, 

The condition for the if statement is again satisfied ( i = 3 is a prime number)

Now the value of the counter increases from 1 to 2 making 3 the second prime number in the sequence. A new variable is created to store the prime number whose value becomes 3, at the end of the if statement the value of the i increases from 3 to 4

Third iteration

Let us recall the values after the second iteration i.e. before the third iteration

counter = 2,

j = 3,

i = 4

During the third iteration

The condition for the if statement is not satisfied and thus the values of the counter variable and the j variable are not changed. 

but the value of i is changed from 4 to 5.

These iterations continue till the n th prime number is reached.

If you want to read this post offline then click here: problem7_projecteuler_matlab.pdf

If you have really understood the above program, then answer these two questions:

How many times did the while loop run?

How many times did the if condition got true while looping?

The above problem has been derived from projecteuler.net and can be found here: problem7

The code was highlighted using hilite.me

Run the program and comment below the output you are getting for a given input.

Keywords: problem 7, projecteuler.net, 10001 prime number, prime number