Problem

big_num=600851475143

limit=int(big_num**0.5) + 1

def sieve(limit):
    if limit < 2:
        return []

    is_prime = [True] * (limit + 1)
    is_prime[0] = is_prime[1] = False

    for p in range(2, int(limit**0.5) + 1):
        if is_prime[p]:
            for multiple in range(p * p, limit + 1, p):
                is_prime[multiple] = False

    prime=[i for i in range(limit+1) if is_prime[i]]
    return prime

my_primes=sieve(limit)
print("the prime numbers are :", my_primes)

print(f"there are {len(my_primes)} prime numbers up to {limit} .")


for p in reversed(my_primes) :
    if big_num%p == 0 :
        print(f"largets prime factor is : {p}")
        break