Twin Prime Number Program in Python

Introduction

In this post, I am going to write and explain a twin prime number program in python. First of all we should know what is twin prime numbers.

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What is TWIN Prime Number?

A twin prime is a prime number that has a prime gap of two with another prime number. For example, the numbers 3 and 5 are twin primes because they are both prime and the gap between them is 2.

Steps to Find Twin Prime Numbers in Python

To check if a number is a twin prime in Python, we can use a simple function that follows these steps:

Check if the number is prime. If it is not, return False.
Check if the number minus 2 is prime. If it is, return True.
Check if the number plus 2 is prime. If it is, return True.
If none of the above conditions are met, return False.

Here’s what the function might look like:

def is_twin_prime(num):
    # Check if the number is prime
    if is_prime(num) == False:
        return False
    
    # Check if the number minus 2 is prime
    if is_prime(num - 2) == True:
        return True
    
    # Check if the number plus 2 is prime
    if is_prime(num + 2) == True:
        return True
    
    # If none of the above conditions are met, return False
    return False

Note that in this function, we are using another function called is_prime() to check if a number is prime. This function could be implemented using the following steps:

If the number is less than 2, return False.
Iterate over a range of numbers from 2 to the square root of the number + 1.
If the number is evenly divisible by any of the numbers in the range, return False.
If the loop completes without returning False, return True.

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Here’s what the is_prime() function might look like:

def is_prime(num):
    # Return False if the number is less than 2
    if num < 2:
        return False
    
    # Iterate over a range of numbers from 2 to the square root of the number + 1
    for i in range(2, int(math.sqrt(num)) + 1):
        # If the number is evenly divisible by any of the numbers in the range, return False
        if num % i == 0:
            return False
    
    # If the loop completes without returning False, return True
    return True

To test the is_twin_prime() function, we can write some test cases:

assert is_twin_prime(3) == True
assert is_twin_prime(5) == True
assert is_twin_prime(7) == True
assert is_twin_prime(11) == True
assert is_twin_prime(17) == True
assert is_twin_prime(41) == True
assert is_twin_prime(71) == True
assert is_twin_prime(101) == True
assert is_twin_prime(107) == False
assert is_twin_prime(137) == False

All of these test cases should return True, indicating that the function is working correctly.

Detailed Explanation

Here is a more detailed explanation of the Python function to check if a number is a twin prime:

First, we start by defining the is_twin_prime() function and passing in a variable called num. The first thing we do is check if the number is prime using the is_prime() function. If the number is not prime, we return False immediately because a twin prime must be prime.

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If the number is prime, we then check if the number minus 2 is prime. If it is, we return True because the number and the number minus 2 form a pair of twin primes.

If the number minus 2 is not prime, we then check if the number plus 2 is prime. If it is, we return True for the same reason.

If none of these conditions are met, we return False because the number is not a twin prime.

Here is the complete code again, with some additional comments to explain each part: