Nth Prime Number

Coding Challenge Level: Beginner

Today's challenge requires you to write code to find the nth prime number of any given index number. This challenge answers the questions, "What is the 10th prime number?", "What is the 100th prime number?" and the list can go on and on.

Solution:

First, let's define what a prime number is. A prime number is a positive integer greater than 1 that has no positive divisors other than 1 and itself. For example, 2, 3, 5, 7, 11, and 13 are the first six prime numbers.

To find the nth prime number, we can use a simple algorithm that checks each positive integer to see if it is prime. If it is prime, we increment a counter until we have found the nth prime number.

Here is the Python code that implements this algorithm:

python

def is_prime(num):
? ? """
? ? This function checks if a number is prime or not.
? ? """
? ? if num <= 1:
? ? ? ? return False
? ? elif num <= 3:
? ? ? ? return True
? ? elif num % 2 == 0 or num % 3 == 0:
? ? ? ? return False
? ? i = 5
? ? while i * i <= num:
? ? ? ? if num % i == 0 or num % (i + 2) == 0:
? ? ? ? ? ? return False
? ? ? ? i += 6
? ? return True


def nth_prime(n):
? ? """
? ? This function finds the nth prime number.
? ? """
? ? count = 0
? ? num = 2
? ? while count < n:
? ? ? ? if is_prime(num):
? ? ? ? ? ? count += 1
? ? ? ? if count == n:
? ? ? ? ? ? return num
? ? ? ? num += 1




# Testing the function
n = 10
print(f"The {n}th prime number is {nth_prime(n)}")        

The is_prime function takes an integer n as input and returns True if n is prime and False otherwise. It checks if n is less than 2, which is not a prime number. Then, it checks if n is divisible by any integer between 2 and the square root of n. If n is divisible by any of these integers, it is not prime and the function returns False. Otherwise, it returns True.

The nth_prime function takes an integer n as input and returns the nth prime number. It initializes a counter variable prime_count to 0 and a variable num to 2, which is the first prime number. It then enters a while loop that checks if num is prime using the is_prime function. If num is prime, the prime_count variable is incremented. If prime_count equals n, then num is the nth prime number and the function returns it. Otherwise, num is incremented and the loop continues.

Let's test the nth_prime function with some example inputs:

>>> nth_prime(6)
13
>>> nth_prime(10)
29
>>> nth_prime(100)
541        

As we can see, the nth_prime function correctly returns the nth prime number for any given input n.

In conclusion, finding the nth prime number can be done easily in Python with the help of a simple algorithm that checks each positive integer to see if it is prime. The is_prime and nth_prime functions we developed are efficient and can handle large values of n.

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