Find nth prime number in python

By Purnendu Das

Hi, today we will learn about how to find an nth prime number in python. Finding a prime number is very easy in python. A prime number is a number which can only be divided by 1 and the number itself.

prime number

Python program to find nth prime number

Code :

n = int(input('Enter : '))
prime_numbers = [2,3]
i=3

if(0<n<3):
    print(n,'th Prime Number is :',prime_numbers[n-1])
elif(n>2):
    while (True):
        i+=1
        status = True
        for j in range(2,int(i/2)+1):
            if(i%j==0):
                status = False
                break
        if(status==True):
            prime_numbers.append(i)
        if(len(prime_numbers)==n):
            break
    print(n,'th Prime Number is :', prime_numbers[n-1])
else:
    print('Please Enter A Valid Number')

Output :

Enter : 10
10 th Prime Number is : 29

Explanation :

• At first, we take the input into the ‘n’ variable.
• We create a python list variable ‘prime_numbers’.
• Initially, we store 2,3 into the ‘prime_numbers’  variable.
• We create an ‘i’ variable.  Initially, we store 3 into the ‘i’ variable.
• We create an if condition. If the value of n is greater than 0 and less than 3, it means if the value of n in between 1 to 2 then the operation will be performed. If the condition satisfied then print the list prime_numbers’s n-1 th position value.
• We create an elif condition. If the value is greater than 2 then the task is performed.
• We create an infinite While Loop. For storing the prime number into the ‘prime_numbers’  variable.
• increase the value of ‘i’ by one.
• We create a boolean variable ‘status’. Initially, it is ‘True’.
• We create a For Loop. The starting value of for loop variable ‘j’ is 2 and ending with (half+1) of the ‘i’ value.  This for loop is used for checking the ‘i’ number is prime or not prime.
• If the remainder of  (‘i’ value / ‘j’ value) is Zero then it not be a prime number. And break the for loop and ‘status‘ will be ‘False’.
• For all value of ‘j’, if the remainder not going to zero then the ‘status‘ will be ‘True’.
• We check if the status True then it is a prime number.  And it stored into the ‘prime_numbers’.
• We check if the length of the list is equal to the ‘n’ value then the while loop will break.
• After breaking the while loop we print the nth prime number.
• We create an else section if the user types any wrong or negative value then program will print ‘Please Enter A Valid Number’.

In this whole process, we can easily find the nth prime number.

You may like to read :

• Catalan Number in Python – Iterative Approach (Factorial)
• Check whether two strings are anagram of each other using Python 3.x or earlier

3 responses to “Find nth prime number in python”

1. Horus Chan says:

   October 19, 2019 at 9:12 pm

   Line 9: why not just use i+=2? It yields the same results.

   Reply
2. Naveen says:

   March 29, 2020 at 2:27 pm

   not need to run upto i/2+1 we can run upto sqrt(i)+1

   Reply
   • Deborah Thompson says:

     February 20, 2022 at 1:15 am

     If not wanting to import math then you can do i**0.5 + 1. Certainly the program runs a lot quicker if not going up to i/2 + 1

     Reply