How to Check if a Number is Prime in Python with Simple Code and Explanation

A prime number is a number that is greater than 1 and has no divisors other than 1 and itself. In this article, you will learn how to write a Python program to check whether a number is prime or not, and we'll explain everything in a simple way.

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🔢 What is a Prime Number?

A prime number has only two factors:

• 1

• The number itself

📌 Examples of prime numbers:

• 2, 3, 5, 7, 11, 13, 17, 19...

📌 Examples of non-prime (composite) numbers:

• 4 (divisible by 2), 6 (divisible by 2 and 3), 9 (divisible by 3)

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💻 Python Program to Check Prime Number

Here’s a simple and clean Python program:

# Program to check if a number is prime

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

# Step 2: Check if the number is less than or equal to 1
if num <= 1:
    print(num, "is not a prime number")
else:
    # Step 3: Use a loop to check for factors
    is_prime = True
    for i in range(2, int(num ** 0.5) + 1):
        if num % i == 0:
            is_prime = False
            break

    # Step 4: Print the result
    if is_prime:
        print(num, "is a prime number")
    else:
        print(num, "is not a prime number")

🧾 Step-by-Step Explanation of the Code

✅ Step 1: Take User Input

num = int(input("Enter a number: "))

• We use input() to ask the user to enter a number.

• int() converts the input from a string to an integer.

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✅ Step 2: Check for Edge Cases

if num <= 1:
    print(num, "is not a prime number")

• A number less than or equal to 1 is not prime (e.g., 0, -5, 1).

• We handle this before doing any further checks.

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✅ Step 3: Check for Factors Using Loop

is_prime = True
for i in range(2, int(num ** 0.5) + 1):
    if num % i == 0:
        is_prime = False
        break

How does this work?

• We assume the number is prime with is_prime = True.

• We check all numbers from 2 to square root of num.

  • Why square root? Because if a number has a factor greater than its square root, it must also have a smaller factor. This reduces the number of checks.

• If we find any number that divides num evenly (num % i == 0), we know it's not a prime.

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✅ Step 4: Show the Result

if is_prime:
    print(num, "is a prime number")
else:
    print(num, "is not a prime number")

• Based on our loop, we print the final result to the user.

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• Based on our loop, we print the final result to the user.

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✅ Example Output

Enter a number: 7
7 is a prime number

Enter a number: 10
10 is not a prime number

🤔 What If We Don’t Use Square Root Optimization?

If we check up to num - 1, the program will still work, but it will be slower, especially for large numbers.

This is the less efficient way:

for i in range(2, num):
    if num % i == 0:
        is_prime = False
        break

📌 Use the square root method for better performance.

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✅ Bonus: Create a Function to Check Prime

You can also make a reusable function to check if a number is prime:

def is_prime(n):
    if n <= 1:
        return False
    for i in range(2, int(n ** 0.5) + 1):
        if n % i == 0:
            return False
    return True

# Test the function
num = int(input("Enter a number: "))
if is_prime(num):
    print(num, "is a prime number")
else:
    print(num, "is not a prime number")

This way, you can reuse the is_prime() function in other programs.

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📚 Summary

• A prime number has only two divisors: 1 and itself.

• We use a for loop to check if the number has any other divisors.

• Using square root optimization improves performance.

• We can also turn the code into a function for reusability.

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🙋‍♂️ Frequently Asked Questions

🔸 Is 1 a prime number?

No, by definition, 1 is not a prime number.

🔸 Why check up to the square root?

Because if a number has a factor greater than its square root, the matching pair factor must be smaller.

🔸 What is the smallest prime number?

The smallest prime number is 2. It is also the only even prime number.