Python Program to Find the Nth Prime Number

Last Updated on 16 March 2025

A prime number is a number that has exactly two factors: 1 and itself. The first few prime numbers are:

In this tutorial, we will write a Python program to find the Nth prime number, where N is a user-defined value.

Python Program to Find the Nth Prime Number

Method 1: Using a Loop and Prime Check

# Function to check if a number is prime
def is_prime(num):
    if num < 2:
        return False
    for i in range(2, int(num ** 0.5) + 1):
        if num % i == 0:
            return False
    return True

# Function to find the Nth prime number
def nth_prime(n):
    count = 0  # Count of prime numbers found
    num = 1  # Starting number to check
    while count < n:
        num += 1
        if is_prime(num):
            count += 1
    return num

# Taking user input
N = int(input("Enter the value of N: "))

# Finding and displaying the Nth prime number
print(f"The {N}th prime number is: {nth_prime(N)}")

Output

Enter the value of N: 5
The 5th prime number is: 11

Method 2: Using a Prime Number List

If you need to find multiple prime numbers efficiently, you can store primes in a list instead of checking each number individually.

def nth_prime(n):
    primes = [2]  # List of found primes
    num = 3  # Start checking from 3
    while len(primes) < n:
        if all(num % p != 0 for p in primes if p * p <= num):
            primes.append(num)
        num += 2  # Skip even numbers
    return primes[-1]

# Taking user input
N = int(input("Enter the value of N: "))

# Finding and displaying the Nth prime number
print(f"The {N}th prime number is: {nth_prime(N)}")

This method is faster because it avoids unnecessary calculations by checking divisibility with only stored primes.