> Please tell me how to vectorize this Python code. Go on, I'm waiting.

Here's a start:

    import numpy as np

    def sieve(limit):
        result = np.ones(limit + 2, dtype=bool)
        result[0] = False
        result[1] = False
        for i in range(2, limit + 1):
            if result[i]:
                yield i
                result[::i] = False

    for prime in sieve(100):
        print(prime)

As you said, you can't vectorize the outer loop because each iteration depends on the result of previous iterations, so I think you can't do too much better than that with this algorithm. (There are a few easy algorithm optimizations, but I think that's kind of orthogonal to your point, and anyway you can do them in any language.)

I would expect there's still a significant performance gap between that and, say, a simple C implementation, but that shouldn't be surprising, and personally I haven't encountered these supposed droves of people claiming that NumPy fully solves the performance gap. From what I've seen there was a general consensus that vectorizing with NumPy can significantly tighten the gap but can rarely fully close it.