Sieve of Eratosthenes

def sieve_of_eratosthenes(limit):
    # Create a boolean list "is_prime" where is_prime[i] is True if i is prime
    is_prime = [True] * (limit + 1)
    is_prime[0] = is_prime[1] = False  # 0 and 1 are not prime numbers

    # Apply the Sieve of Eratosthenes
    for i in range(2, int(limit**0.5) + 1):
        if is_prime[i]:
            for j in range(i**2, limit + 1, i):
                is_prime[j] = False

    # Use list comprehension to extract prime numbers
    primes = [num for num in range(2, limit + 1) if is_prime[num]]

    return primes

# Example: Generate a list of primes up to 50
limit = 50
prime_numbers = sieve_of_eratosthenes(limit)

print("Prime Numbers up to", limit, ":", prime_numbers)