## A function to check weather a number is prime or not
def isPrime(number, i=2):
    #Exclude zero and one
    if number <= 0 or number == 1:
        return False
    #Check if i is equal to the number if thats the case then we have exhausted the list of integers to check against
    #Declare number prime
    if number == i:
        return True
    #Check if the number is divisble by i
    if number % i == 0:
        return False
    #increment i and call the function again.
    return isPrime(number, i+1)

## A function to find all prime numbers in the given range and retun them in a list
def prime_in_range(min_value, max_value):
    prime = []
    """
    Every prime number except two and three can be represented as 6n+1 and 6n-1 where n is a natural number.
    So, rather than checking all numbers in the range we are going to check numbers that satisfy the above equations.
    """
    min_n = ((min_value + 1) // 6)
    max_n = ((max_value + 1) // 6)
    ## Check weather to include 2 and 3 in the list.
    if min_value <= 2 and max_value >= 2:
        prime = prime + [2]
    
    if min_value <= 3 and max_value >= 3:
        prime = prime + [3]
    
    ## Check extreme cases separately to exclude lower than min and larger than max values
    number1 = (6 * min_n - 1)
    number2 = (6 * min_n + 1)
    ## Check if the numbers are prime using the function written above
    if number1 >= min_value and isPrime(number1):
        prime = prime + [number1]
    if isPrime(number2):
        prime = prime + [number2]
    ## Add all other prime numbers to the list.    
    for i in range(min_n + 1, max_n):
        number1 = (6 * i - 1)
        number2 = (6 * i + 1)
        ## Check if the numbers are prime using the function written above
        if isPrime(number1):
            prime = prime + [number1]
        if isPrime(number2):
            prime = prime + [number2]
            
    ## Check extreme cases separately to exclude lower than min and larger than max values
    number1 = (6 * max_n - 1)
    number2 = (6 * max_n + 1)
    ## Check if the numbers are prime using the function written above
    if number2 <= max_value and isPrime(number1):
        prime = prime + [number1]
    if isPrime(number1):
        prime = prime + [number2]
    return prime
    

## Main Program to call the above function
if __name__ == "__main__":
    ## Ask the user for input
    min_value = int(input('Please Enter Minimum Value: '))
    max_value = int(input('Please Enter Maximum Value: '))
    
    prime = prime_in_range(min_value, max_value)
    if prime == []:
        print("No prime numbers in the range")
    else:
        print("The following are prime numbers in the range")
        print(prime)