Cousin Primes in Python

🔍 Exploring Cousin Primes with Python

🎯 What Are Cousin Primes?

Cousin primes are pairs of prime numbers that differ by exactly 4. Examples include (3, 7), (7, 11), and (13, 17). These pairs are part of the broader study of prime gaps and distributions in number theory.

💡 Our Goal

We’ll write a Python program that:

• Checks if a number is prime
• Scans numbers up to a given limit
• Finds and displays all cousin 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_cousin_primes(limit=1000):
    cousin_pairs = []
    for p in range(2, limit - 4):
        if is_prime(p) and is_prime(p + 4):
            cousin_pairs.append((p, p + 4))
    return cousin_pairs

# Run the function and print results
cousins = find_cousin_primes(1000)
print("Cousin Prime Pairs up to 1000:")
for pair in cousins:
    print(pair)

Copy and Try it here!

📊 Sample Output

Output:

Cousin Prime Pairs up to 1000:
(3, 7)
(7, 11)
(13, 17)
(19, 23)
(37, 41)
(43, 47)
(67, 71)
(73, 77)
...

🔍 Why It’s Interesting

Unlike twin primes (which differ by 2), cousin primes offer a slightly wider gap, yet still show intriguing patterns. Studying these pairs helps us understand how primes are spaced and whether certain gaps are more frequent.

🌟 Final Thoughts

Try changing the limit and observe how cousin primes behave. Are they more frequent in certain ranges? Do they cluster? This simple script is a great way to explore prime behavior and prepare for deeper number theory investigations.