How to Check if a Number is Prime in Python 🐍

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Check if a Number is Prime in Python

A prime number is a number greater than 1 that is divisible only by 1 and itself. Prime numbers are significant in various fields, including cryptography and number theory. In this blog, we will learn how to check if a given number is prime using Python.

By the end of this post, you will understand:

  • What a prime number is.
  • How to write an efficient Python program to check if a number is prime.

What is a Prime Number?

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. For example:

  • Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19…
  • Non-prime numbers (also called composite numbers): 4, 6, 8, 9, 12…

A key property of prime numbers is that they have exactly two distinct divisors: 1 and the number itself.

How to Check if a Number is Prime

To check if a number is prime, we need to determine if it has any divisors other than 1 and itself. This can be done by trying to divide the number by all integers from 2 to the square root of the number.

Method 1: Checking Prime Using a Simple For Loop

This is the most straightforward way to check if a number is prime. We’ll loop through numbers starting from 2 up to n-1 and check if any of them divide n evenly.

Code Example:

# Program to check if a number is prime

# Step 1: Take user input
number = int(input("Enter a number: "))

# Step 2: Check if the number is prime
if number > 1:
    for i in range(2, number):
        if (number % i) == 0:
            print(f"{number} is not a prime number.")
            break
    else:
        print(f"{number} is a prime number.")
else:
    print(f"{number} is not a prime number.")

Explanation of the Code:

  1. User Input:
  • The user is prompted to enter a number, which is stored in the variable number.
  1. For Loop:
  • We start by checking if the number is greater than 1 (since numbers less than or equal to 1 are not prime).
  • The loop checks if any number between 2 and number-1 divides the input number evenly. If a divisor is found, the number is not prime, and the loop stops.
  1. Else Clause:
  • If no divisors are found in the loop, the number is prime.

Sample Output:

Enter a number: 29
29 is a prime number.
Enter a number: 12
12 is not a prime number.

Method 2: Optimized Prime Check (Using Square Root)

We can optimize the prime-checking process by only looping up to the square root of the number. If a number is divisible by any number up to its square root, it is not a prime number.

Code Example:

# Program to check if a number is prime (optimized version)

# Step 1: Import math module to use sqrt function
import math

# Step 2: Take user input
number = int(input("Enter a number: "))

# Step 3: Optimized check for prime number
if number > 1:
    for i in range(2, int(math.sqrt(number)) + 1):
        if (number % i) == 0:
            print(f"{number} is not a prime number.")
            break
    else:
        print(f"{number} is a prime number.")
else:
    print(f"{number} is not a prime number.")

Explanation of the Code:

  1. Square Root Optimization:
  • Instead of checking divisors up to n-1, we only check up to sqrt(n). This is because if a number is divisible by any number larger than its square root, the corresponding divisor will be smaller than the square root.
  1. Math Module:
  • We use the math.sqrt() function to calculate the square root of the number and loop only up to that value.

Sample Output:

Enter a number: 31
31 is a prime number.
Enter a number: 25
25 is not a prime number.

Method 3: Using a Function to Check Prime Numbers

We can encapsulate the logic for checking prime numbers inside a function. This makes the code more reusable and easier to maintain.

Code Example:

# Program to check if a number is prime using a function

# Step 1: Define a function to check prime
def is_prime(number):
    if number > 1:
        for i in range(2, int(number ** 0.5) + 1):
            if (number % i) == 0:
                return False
        return True
    else:
        return False

# Step 2: Take user input
number = int(input("Enter a number: "))

# Step 3: Call the function and display the result
if is_prime(number):
    print(f"{number} is a prime number.")
else:
    print(f"{number} is not a prime number.")

Explanation of the Code:

  1. Function Definition:
  • We define a function is_prime() that takes an integer as input and returns True if the number is prime and False otherwise.
  1. Function Call:
  • After taking the user input, we call the is_prime() function and print whether the number is prime or not.

Sample Output:

Enter a number: 17
17 is a prime number.

Method 4: Prime Check Using Python Libraries

There are libraries like SymPy that can help us check prime numbers efficiently. If you’re using external libraries in your project, this can be an easy way to check prime numbers.

Code Example:

# Program to check if a number is prime using sympy library

# Step 1: Import sympy's isprime function
from sympy import isprime

# Step 2: Take user input
number = int(input("Enter a number: "))

# Step 3: Use isprime function to check if the number is prime
if isprime(number):
    print(f"{number} is a prime number.")
else:
    print(f"{number} is not a prime number.")

Explanation of the Code:

  1. SymPy Library:
  • SymPy is a Python library for symbolic mathematics, and it has a built-in function isprime() to check if a number is prime.
  1. Prime Check:
  • The isprime() function takes a number as input and returns True if the number is prime and False otherwise.

Conclusion

In this blog, we explored several ways to check if a number is prime in Python:

  1. Using a basic for loop to check divisors.
  2. Optimizing the prime check using the square root of the number.
  3. Encapsulating the prime check logic inside a function.
  4. Using the SymPy library for a more efficient solution.

Understanding prime numbers and how to check them is fundamental in various areas of computer science. Try these methods out in your Python programs and choose the one that best fits your needs!

Stay tuned for more Python programming tutorials! 😊

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