Please describe what the following code does and (if applicable how it works):
import math
def prime_sieve(num: int) -> list[int]: if num <= 0: raise ValueError(f""num: Invalid input, please enter a positive integer."")
sieve = [True] * (num + 1) prime = [] start = 2 end = int(math.sqrt(num))
while start <= end: if sieve[start] is True: prime.append(start) for i in range(start * start, num + 1, start): if sieve[i] is True: sieve[i] = False start += 1
for j in range(end + 1, num + 1): if sieve[j] is True: prime.append(j)
return prime
Description:
The code above defines a function called prime_sieve(), which takes a numeric value num as an argument, and returns a list containing all prime numbers between 2 and num.
The function first checks the input argument to ensure that it is a positive integer. Then, it creates an array sieve made up of True values, with one value in each index from 2 to num. Next, a list prime is created, initializing it with the value 2. Then, the loop beginning at start and ending at end iterates through the values in the sieve array, checking each value to see if it is True. If it is, the value is appended to the list prime. Finally, the value of start is incremented, and the loop reiterates until all the elements in the sieve array are checked. At that point, the list contains all of the prime numbers between 2 and num.