🔢 Counting Twin Primes with Python

🎯 What Are Twin Primes?

Twin primes are pairs of prime numbers that differ by exactly 2. Examples include (3, 5), (11, 13), and (17, 19). These pairs are a fascinating topic in number theory and are still part of unsolved mathematical mysteries.

💡 Our Goal

We’ll write a Python program that:

• Checks if a number is prime
• Scans a range of numbers
• Counts and displays all twin prime pairs

💻 Python Code

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

def count_twin_primes(start, end):
    count = 0
    twin_pairs = []
    for i in range(start, end - 1):
        if is_prime(i) and is_prime(i + 2):
            count += 1
            twin_pairs.append((i, i + 2))
    return count, twin_pairs

# 🚀 User Input
try:
    start_range = int(input("Enter starting range: "))
    end_range = int(input("Enter ending range: "))

    if start_range >= end_range:
        print("❌ Starting range must be less than ending range.")
    else:
        total, pairs = count_twin_primes(start_range, end_range)
        print(f"\n✅ Total twin prime pairs between {start_range} and {end_range}: {total}")
        for a, b in pairs:
            print(f"({a}, {b})")
except ValueError:
    print("❌ Please enter valid integers.")

Copy and Try it here!

📊 Sample Output

Input: 10 to 50

Output:

✅ Total twin prime pairs between 10 and 50: 4
(11, 13)
(17, 19)
(29, 31)
(41, 43)

🔍 Why It’s Useful

This script is a great way to explore prime distributions and test hypotheses about their frequency. It’s also a handy tool for CSIR NET preparation or any number theory project.

🌟 Final Thoughts

Try different ranges and observe how twin primes behave. Are they more frequent in smaller ranges? Do they thin out as numbers grow? This simple tool opens the door to deeper mathematical exploration.