Eratosthenes的筛子认为127之后的所有数字都是素数

Question

I'm running into problems with my Sieve of Eratosthenes. I wanted to write a Sieve that didn't require an array of all numbers up to the largest prime you want, instead just keeping track of each prime multiple as the Sieve reaches it. That means you don't have to do all the work up front, but can just determine the next prime when you need it. It would also be easy to add interface features like "find K primes starting at N". Here is the pseudocode:

Begin with current number set to 2
Loop:
    If prime queue is not empty:
        Peek at the top prime in the queue
        If current > top, we can move top to the next multiple
            Remove the top prime from the prime queue
            Increment top to its next multiple
            Re-add it to the queue
        If current == top, current is not a prime
            Increment current number to next integer
        If current < top, we've found a prime
            Break
Push current number onto prime queue
Increment current number to next integer
Return the new prime

So here's the problem: I correctly calculate the first 31 primes (up to 127), but after that it thinks every number is prime. I've put my code on Ideone -- I'm hoping it's some Java collections behavior, or a trivial bug, rather than the algorithm itself. I can't think of a reason the algorithm should break after a certain number of primes. I've confirmed manually that after 127, if the heap is properly ordered, my algorithm should recognize 128 as not a prime, but that's not what the code shows me.

Any suggestions?

http://ideone.com/E07Te

(I will, of course, increment by 2 (to skip all non-prime even numbers) once I get the basic algorithm working. I'll probably also make the Sieve an iterable.)

Answer 1

Your problem is

top.multiple == current

in connection with

Integer current = 2;
Integer multiple;

There is a cache of Integer s with small absolute value, -128 to 127 , if I recall correctly, so the comparison using == compares identical instances for values smaller than 128. But from 128 on, you get a new boxed Integer for current , and that is a different object than the one referenced by top.multiple .

Compare using equals or declare int current; to solve it.

And improve your algorithm, note multiples of each prime only from the prime's square.

Answer 2

You're not checking your whole list:

Sieve heap after 31: [[127:127], [11:132], [2:128]

You get to 132, which is > 128, and thus hit the break; before you check for 2*64.