How to implement an efficient infinite generator of prime numbers in Python?

Question

This is not a homework, I am just curious.

INFINITE is the key word here.

I wish to use it as for p in primes(). I believe that this is a built-

Answer 1

Here is a simple but not terribly slow one using a heap instead of a dict:

import heapq

def heap_prime_gen_squares(): 
    yield 2  
    yield 3  
    h = [(9, 6)]
    n = 5
    while True:
        a, b = h[0]
        while n < a:
            yield n
            heapq.heappush(h, (n * n, n << 1))
            n += 2
        heapq.heapreplace(h, (a + b, b))  # Replace h[0], which is still (a, b).

My speed measurements of user time for the first 1 million primes (smaller numbers are better):

• postponed_sieve (dict-based): 8.553s
• erat2b (dict-based): 9.513s
• erat2a (dict-based): 10.313s
• heap_prime_gen_smallmem (heap-based): 23.935s
• heap_prime_gen_squares (heap-based): 27.302s
• heapprimegen (dict-based): 145.029s

So dict-based approaches seem to be the fastest.