Question

有人可以告诉我为什么我的程序输出所有素数到输入的n以及数字n+2（无论是否是素数）？如果它是素数，有时也会n+1，例如输入n=10时，输出为2,3,5,7,11,12。

这是我的代码：

/*Write a program that reads in a number n between 1 and 100,000 and then lists all the prime numbers between 1 and n inclusive.*/

#include

#define LIMIT 100000 /*size of integers array*/
#define PRIMES 100000 /*size of primes array*/

int main(){
    int i,j,numbers[LIMIT];
    int primes[PRIMES];
    int n, count;
    count = 0;

    /*Read in an upper limit, n*/
    printf("Please enter a value for n: ");
    if (scanf("%d", &n) !=1) {
        printf("Sorry, cannot read n.\n");
        return 1;
    }

    /*fill the array with natural numbers*/
    for (i=0;i<=n;i++){
        numbers[i]=i+2;
    }

    /*sieve the non-primes*/
    for (i=0;i<=n;i++){
        if (numbers[i]!=-1){
            for (j=2*numbers[i]-2;j<n;j+=numbers[i])
                numbers[j]=-1;
        }
    }

    /*transfer the primes to their own array*/
    j = 0;
    for (i=0;i<=n&&j<PRIMES;i++)
        if (numbers[i]!=-1) {
            primes[j++] = numbers[i];
            count = count + 1; }

    /*print*/
    for (i=0;i<count;i++)
        printf("%d\n",primes[i]);

    return 0;
}

Answer 1

你总是在你的数字数组中加上n + 1和n + 2，

for (i=0;i<=n;i++){
    numbers[i]=i+2;
}

对于我在{n-1，n}。

但你不能过滤掉它们，因为这个循环：

for (i=0;i<=n;i++){
    if (numbers[i]!=-1){
        for (j=2*numbers[i]-2;j<n;j+=numbers[i])
            numbers[j]=-1;
    }
}

忽略大于n的数字。

工作版本：

#define MAX_SIZE 100000 /*size of integers array*/

int main() {
    unsigned int i; 
    unsigned int j;
    unsigned int max_filled_index;
    unsigned int numbers[MAX_SIZE];
    unsigned int primes[MAX_SIZE];
    unsigned int num_to_sieve;
    unsigned int prime_count = 0;

    /*Read in an upper limit, n*/
    printf("Please enter a value for n: ");
    if (scanf("%d", &num_to_sieve) != 1) {
        printf("Sorry, cannot read n.\n");
        return 1;
    }

    max_filled_index = num_to_sieve - 2;
    /*fill the array with natural numbers*/
    for (i = 0; i <= max_filled_index; i++) {
        numbers[i] = i + 2;
    }


    /*sieve the non-primes*/
    for (i = 0; i <= max_filled_index; i++) {
        if (numbers[i] != 0) {
            for (j = 2 * numbers[i] - 2; j <= max_filled_index; j += numbers[i]) {
                numbers[j] = 0;
            }
        }
    }

    /*transfer the primes to their own array*/
    for (i = 0; i <= max_filled_index && prime_count < MAX_SIZE; i++)
        if (numbers[i] != 0) {
            primes[prime_count] = numbers[i];
            prime_count++;
        }

    /*print*/
    for (i = 0; i < prime_count; i++)
        printf("%d\n", primes[i]);

    return 0;
}

Erastothenes筛选的C代码

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