计算第K个素数

暂时没有时间整理，先放在这里：

http://www.quora.com/Prime-Numbers/What-are-good-ways-to-find-nth-prime-number-in-the-fastest-way

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This is an algorithm to test whether or not a given integer is prime. It's called the AKS primality test http://en.m.wikipedia.org/wiki/A...

And can be done in polynomial time, which is usually considered a decent amount of time.

Now if you're trying to compute the nth prime, it has been proven that the nth prime must be greater than



and less than



When . So if you're searching for the nth prime, I'd look in this gap.

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If it is an interview question, I believe Sieve of Eratosthenes algorithm is a pretty good answer. For not too large n, the algorithm should work fine. For extremely large n, then you probably have to use a precomputed array of bins. Each covers a range of [i*N-i*(N+1)-1] and the number of prime numbers in that range as described in [2].

There is no general formula to compute nth prime number.

[1] http://en.wikipedia.org/wiki/Sie...
[2] http://primes.utm.edu/nthprime/a...

  

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附上一个同学写的用bitarray实现的http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes求素数的方法：

/*
 * ========================================================================
 *
 *       Filename:  bitset.h
 *
 *    Description:  bitset implementation in c.
 *
 *        Created:  05/27/2013 11:09:43 PM
 *
 *         Author:  Fu Haiping (forhappy), haipingf@gmail.com
 *        Company:  ICT ( Institute Of Computing Technology, CAS )
 *
 * ========================================================================
 */
#include <limits.h>     /* for CHAR_BIT */

#define BITMASK(b) (1 << ((b) % CHAR_BIT))
#define BITSLOT(b) ((b) / CHAR_BIT)
#define BITSET(a, b) ((a)[BITSLOT(b)] |= BITMASK(b))
#define BITCLEAR(a, b) ((a)[BITSLOT(b)] &= ~BITMASK(b))
#define BITTEST(a, b) ((a)[BITSLOT(b)] & BITMASK(b))
#define BITNSLOTS(nb) ((nb + CHAR_BIT - 1) / CHAR_BIT)
/* 
 * char bitarray[BITNSLOTS(47)];
 * BITSET(bitarray, 23);
 * if(BITTEST(bitarray, 35)) ...
 *
 * */

#include <stdio.h>
#include <string.h>

#define MAX 10000

int main()
{
    char bitarray[BITNSLOTS(MAX)];
    int i, j;

    memset(bitarray, 0, BITNSLOTS(MAX));

    for(i = 2; i < MAX; i++) {
        if(!BITTEST(bitarray, i)) {
            printf("%d\n", i);
            for(j = i + i; j < MAX; j += i)
                BITSET(bitarray, j);
        }
    }
    return 0;
}