Write A Python Function To Find The Prime Numbers in Range

Throughout history, prime numbers have intrigued mathematicians and captivated explorers of numerical realms. These indivisible guardians of the number line hold mysteries that continue to inspire exploration. Today, we'll embark on our own journey to uncover prime numbers using the power of Python.

 

Prime Function

Here's a Python function that reveals the prime numbers within a chosen range, meticulously crafted for efficiency:

Python

import math

def find_primes(lower, upper):
    """Embarks on a quest to discover prime numbers within the specified range,
    utilizing tactics for optimized performance.

    Args:
        lower: The starting point of our prime number expedition (inclusive).
        upper: The final destination of our numerical voyage (inclusive).

    Returns:
        A treasure trove of prime numbers unearthed within the given bounds.
    """

    primes = []  # A vessel to store our prime discoveries

    # Ensure our journey begins at the true frontier of prime numbers
    if lower <= 1:
        lower = 2

    # Traverse the numerical landscape
    for num in range(lower, upper + 1):
        is_prime = True  # Assume primeness until proven otherwise

        # Engage in optimized divisibility checks, seeking potential divisors
        for i in range(2, int(math.sqrt(num)) + 1):
            if num % i == 0:
                is_prime = False  # Alas, a divisor has been found
                break  # Cease further division attempts for this number

            # Further optimization: swiftly bypass even divisors beyond 2
            if i > 2 and i % 2 == 0:
                continue

        # If primeness remains intact, add this numerical gem to our collection
        if is_prime:
            primes.append(num)

    return primes  # Return the fruits of our numerical expedition

# Embark on our first prime number quest!
lower = 10
upper = 50
primes = find_primes(lower, upper)
print(primes)  # Unveil the prime numbers within our chosen realm: [11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]

 

Explanation:

1. Import math: This imports the math module for the sqrt function.
2. find_primes(lower, upper): This function takes two arguments: the lower and upper bounds of the range.
3. Prime list: An empty list primes is created to store the prime numbers found.
4. Handle lower bound: If lower is less than or equal to 1, it's set to 2 as primes start from 2.
5. Iteration through range: The for loop iterates through each number from lower to upper.
6. Prime check: The is_prime flag is initially set to True for each number.
7. Optimized divisibility checks:
   • The for loop checks for divisibility only up to the square root of num, optimizing the process.
   • It skips even divisors after 2, further improving efficiency.
   • If a divisor is found, is_prime is set to False and the loop breaks.
8. Append prime numbers: If is_prime remains True after the checks, the number is appended to the primes list.
9. Return prime list: The function returns the list of prime numbers found.

 

Conclusion

We've successfully harnessed Python to uncover prime numbers, venturing into the heart of numerical patterns. This journey has revealed:

• The elegance of prime numbers as fundamental building blocks of the number system.
• The power of Python to explore mathematical concepts efficiently.
• The importance of optimization techniques for computational tasks.

As we continue exploring prime numbers and their applications, Python remains a steadfast companion, ready to illuminate new discoveries.