my code takes 2 milliseconds to execute from tip to tail ...

600851475143

import math

import time

number = int(input("> "))

start_time = time.time()

def prime_factors(number):

prime_factorization = []

box = number

while number > 1:
    for i in range(math.floor(math.log2(number))):
        for j in range(2, number + 1):
            if number % j == 0:
                prime_factorization.append(j)
                number = number//j
                last_factor = j
                if last_factor > math.sqrt(box):
                    return prime_factorization
                break
return prime_factorization

print(f"Prime factors = {prime_factors(number)}")

print(f"execution time = {time.time() - start_time} seconds")

My code takes 2 milliseconds to execute from tip to tail ...

# 600851475143

import math

import time

number = int(input("> "))

start_time = time.time()


def prime_factors(number):

    prime_factorization = []

    box = number

    while number > 1:
        for i in range(math.floor(math.log2(number))):
            for j in range(2, number + 1):
                if number % j == 0:
                    prime_factorization.append(j)
                    number = number//j
                    last_factor = j
                    if last_factor > math.sqrt(box):
                        return prime_factorization
                    break
    return prime_factorization


print(f"Prime factors = {prime_factors(number)}")

print(f"execution time = {time.time() - start_time} seconds")