times_genPrimes.py

def genPrimes(n):
    found = []
    found_lo = []
    for x in range(2,n+1):
        yas = True
        for y in found_lo:
            if x%y == 0:
                yas = False
                break
        if yas:
            found.append(x)
            if x <= n**0.5:
                found_lo.append(x)
    return found

def genPrimes_set(n):
    found = []
    found_lo = set()
    for x in range(2,n+1):
        yas = True
        for y in found_lo:
            if x%y == 0:
                yas = False
                break
        if yas:
            found.append(x)
            if x <= n**0.5:
                found_lo.add(x)
    return found


import timeit

print(min(timeit.Timer(lambda: genPrimes(1000000)).repeat(10, 1)))
print(min(timeit.Timer(lambda: genPrimes_set(1000000)).repeat(10, 1)))
#>>> 1.1185914840025362
#>>> 1.354676898001344

times_primes_raw.py

def primes_raw(n):
    result = set(range(2, n + 1))
    div = 2
    while div * div <= n:
        if div in result:
            result.difference_update(range(div * 2, n + 1, div))
        div += 1
    return sorted(result)

def primes_raw_lst(n):
    result = [True] * (n + 1)
    result[0] = result[1] = False

    div = 2
    while div * div <= n:
        if result[div]:
            for x in range(div * 2, n + 1, div):
                result[x] = False
        div += 1
    return result

def primes_raw_lst_fast(n):
    result = [True] * (n + 1)
    result[0] = result[1] = False

    div = 2
    while div * div <= n:
        if result[div]:
            result[div * 2::div] = [0] * len(range(div * 2, n + 1, div))
        div += 1
    return result


import timeit

print(min(timeit.Timer(lambda: primes_raw(1000000)).repeat(10, 10)))
print(min(timeit.Timer(lambda: primes_raw_lst(1000000)).repeat(10, 10)))
print(min(timeit.Timer(lambda: primes_raw_lst_fast(1000000)).repeat(10, 10)))
#>>> 2.0144221499940613
#>>> 1.204771492004511
#>>> 0.23468445800244808