python寻找素数_在python中寻找素数

我知道python“慢得像脏东西”，但我想做一个快速而高效的程序来找到素数。这就是我所拥有的：num = 5 #Start at five, 2 and 3 are printed manually and 4 is a multiple of 2

print("2")

print("3")

def isPrime(n):

#It uses the fact that a prime (except 2 and 3) is of form 6k - 1 or 6k + 1 and looks only at divisors of this form.

i = 5

w = 2

while (i * i <= n): #You only need to check up too the square root of n

if (n % i == 0): #If n is divisable by i, it is not a prime

return False

i += w

w = 6 - w

return True #If it isn´t ruled out by now, it is a prime

while True:

if ((num % 2 != 0) and (num % 3 != 0)): #save time, only run the function of numbers that are not multiples of 2 or 3

if (isPrime(num) == True):

print(num) #print the now proved prime out to the screen

num += 2 #You only need to check odd numbers

现在我的问题是：

-这会打印出所有的质数吗？

-这会打印出不是素数的数字吗？

-有没有更有效的方法？

-这将发展到什么程度(python的限制)，有什么方法可以提高上限吗？在

使用python 2.7.12