Sieve of Eratosthenes - Finding Primes Python

Question

Just to clarify, this is not a homework problem :)

I wanted to find primes for a math application I am building & came across Sieve of Eratosthenes approach.

Answer 1

not sure if my code is efficeient, anyone care to comment?

from math import isqrt

def isPrime(n):
    if n >= 2: # cheating the 2, is 2 even prime?
        for i in range(3, int(n / 2 + 1),2): # dont waste time with even numbers
            if n % i == 0:
                return False
    return True

def primesTo(n): 
    x = [2] if n >= 2 else [] # cheat the only even prime
    if n >= 2:
        for i in range(3, n + 1,2): # dont waste time with even numbers
            if isPrime(i):
                x.append(i)  
    return x

def primes2(n): # trying to do this using set methods and the "Sieve of Eratosthenes"
    base = {2} # again cheating the 2
    base.update(set(range(3, n + 1, 2))) # build the base of odd numbers
    for i in range(3, isqrt(n) + 1, 2): # apply the sieve
        base.difference_update(set(range(2 * i, n + 1 , i)))
    return list(base)

print(primesTo(10000)) # 2 different methods for comparison
print(primes2(10000))