Twin Primes Finder: A Python Exploration

🔍 Discovering Twin Primes with Python

🎯 What Are Twin Primes?

Twin primes are pairs of prime numbers that differ by exactly 2. For example, (3, 5), (11, 13), and (17, 19) are all twin primes. These pairs are fascinating in number theory and have deep implications in the study of prime gaps and distribution.

🧠 Our Strategy

We’ll write a Python program that:

• Checks if a number is prime
• Scans a range of numbers
• Finds and prints 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 find_twin_primes(start, end):
    twin_primes = []
    for i in range(start, end - 1):
        if is_prime(i) and is_prime(i + 2):
            twin_primes.append((i, i + 2))
    return twin_primes

# 🚀 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:
        twins = find_twin_primes(start_range, end_range)
        print(f"\nTwin primes between {start_range} and {end_range}:")
        for pair in twins:
            print(pair)
        if not twins:
            print("No twin primes found in this range.")
except ValueError:
    print("❌ Please enter valid integers.")

Copy and Try it here!

📌 How It Works

• is_prime(n): Checks if n is divisible by any number up to √n
• find_twin_primes(start, end): Iterates through the range and checks if both i and i + 2 are prime
• User inputs define the range to search for twin primes

📊 Sample Output

If you input start = 1 and end = 20, the output will be:

Twin primes between 1 and 20:
(3, 5)
(5, 7)
(11, 13)
(17, 19)

🧮 Why It Matters

Twin primes are not just mathematical curiosities—they’re part of unsolved problems like the Twin Prime Conjecture, which asks whether infinitely many such pairs exist. This simple Python tool lets you explore their distribution and patterns interactively.

🌟 Final Thoughts

Whether you're preparing for CSIR NET, exploring number theory, or just curious about primes, this twin prime finder is a great way to blend programming with pure mathematics. Try different ranges and see what patterns emerge!