c语言编写 1编写程序用筛选法找素数。2编写程序用6N+1法找素数。 3编写程序用除余法找素数。 4编写程序用遍历二维数组中素数。 5编写程序筛万内的素数--二用筛法。 6编写程序验证哥特巴赫猜想一三用筛法。 7编写程序找费马"二平方"素数一"滚雪球"式地得到所使用的素数。 8编写程序找回文式素数一依然含有诸多猜想。 9编写程序找双向环形素数-循环移位组数判断。 10编写菜单完成程序调用和退出。

1. 筛选法找素数：

#include <stdio.h>

int main()
{
    int n, i, j, flag;
    printf("Enter the value of n: ");
    scanf("%d", &n);
    printf("Prime numbers from 1 to %d are: ", n);

    for (i = 2; i <= n; i++) {
        flag = 1;
        for (j = 2; j <= i / 2; j++) {
            if (i % j == 0) {
                flag = 0;
                break;
            }
        }
        if (flag == 1) {
            printf("%d ", i);
        }
    }

    return 0;
}

2. 6N+1法找素数：

#include <stdio.h>
#include <math.h>

int main()
{
    int n, i, j, flag;
    printf("Enter the value of n: ");
    scanf("%d", &n);
    printf("Prime numbers from 1 to %d are: ", n);

    for (i = 2; i <= n; i++) {
        flag = 1;
        if (i == 2 || i == 3) {
            printf("%d ", i);
            continue;
        }
        if (i % 6 != 1 && i % 6 != 5) {
            continue;
        }
        for (j = 2; j <= sqrt(i); j++) {
            if (i % j == 0) {
                flag = 0;
                break;
            }
        }
        if (flag == 1) {
            printf("%d ", i);
        }
    }

    return 0;
}

3. 除余法找素数：

#include <stdio.h>
#include <math.h>

int main()
{
    int n, i, j, flag;
    printf("Enter the value of n: ");
    scanf("%d", &n);
    printf("Prime numbers from 1 to %d are: ", n);

    for (i = 2; i <= n; i++) {
        flag = 1;
        for (j = 2; j <= sqrt(i); j++) {
            if (i % j == 0) {
                flag = 0;
                break;
            }
        }
        if (flag == 1) {
            printf("%d ", i);
        }
    }

    return 0;
}

4. 遍历二维数组中素数：

#include <stdio.h>
#include <math.h>

int isPrime(int n)
{
    int i;
    if (n == 2 || n == 3) {
        return 1;
    }
    if (n % 6 != 1 && n % 6 != 5) {
        return 0;
    }
    for (i = 2; i <= sqrt(n); i++) {
        if (n % i == 0) {
            return 0;
        }
    }
    return 1;
}

int main()
{
    int arr[3][3] = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
    int i, j;

    printf("Prime numbers in the array: ");
    for (i = 0; i < 3; i++) {
        for (j = 0; j < 3; j++) {
            if (isPrime(arr[i][j])) {
                printf("%d ", arr[i][j]);
            }
        }
    }

    return 0;
}

5. 筛法找素数：

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

int main()
{
    int n, i, j;
    printf("Enter the value of n: ");
    scanf("%d", &n);

    int primes[n + 1];
    memset(primes, 1, sizeof(primes));

    for (i = 2; i * i <= n; i++) {
        if (primes[i]) {
            for (j = i * i; j <= n; j += i) {
                primes[j] = 0;
            }
        }
    }

    printf("Prime numbers from 1 to %d are: ", n);
    for (i = 2; i <= n; i++) {
        if (primes[i]) {
            printf("%d ", i);
        }
    }

    return 0;
}

6. 哥特巴赫猜想验证：

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

int isPrime(int n)
{
    int i;
    if (n == 2 || n == 3) {
        return 1;
    }
    if (n % 6 != 1 && n % 6 != 5) {
        return 0;
    }
    for (i = 2; i * i <= n; i++) {
        if (n % i == 0) {
            return 0;
        }
    }
    return 1;
}

int main()
{
    int n, i, j, flag;
    printf("Enter the value of n: ");
    scanf("%d", &n);

    int primes[n + 1];
    memset(primes, 1, sizeof(primes));

    for (i = 2; i * i <= n; i++) {
        if (primes[i]) {
            for (j = i * i; j <= n; j += i) {
                primes[j] = 0;
            }
        }
    }

    printf("Goldbach conjecture numbers from 4 to %d: ", n);
    for (i = 4; i <= n; i += 2) {
        flag = 0;
        for (j = 2; j <= i / 2; j++) {
            if (primes[j] && primes[i - j]) {
                flag = 1;
                printf("(%d,%d) ", j, i - j);
                break;
            }
        }
        if (flag == 0) {
            printf("Goldbach conjecture is false for %d", i);
            break;
        }
    }

    return 0;
}

7. 滚雪球式找素数：

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

int main()
{
    int n, i, j, k, flag;
    printf("Enter the value of n: ");
    scanf("%d", &n);

    int primes[n + 1];
    memset(primes, 1, sizeof(primes));

    for (i = 2; i * i <= n; i++) {
        if (primes[i]) {
            for (j = i * i; j <= n; j += i) {
                primes[j] = 0;
            }
        }
    }

    printf("Prime numbers from 1 to %d: 2 ", n);
    for (i = 1; i <= n / 6; i++) {
        for (j = -1; j <= 1; j += 2) {
            k = 6 * i + j;
            if (k > n) {
                break;
            }
            if (primes[k]) {
                printf("%d ", k);
            }
        }
    }

    return 0;
}

8. 回文式素数：

#include <stdio.h>
#include <math.h>

int isPrime(int n)
{
    int i;
    if (n == 2 || n == 3) {
        return 1;
    }
    if (n % 6 != 1 && n % 6 != 5) {
        return 0;
    }
    for (i = 2; i <= sqrt(n); i++) {
        if (n % i == 0) {
            return 0;
        }
    }
    return 1;
}

int isPalindrome(int n)
{
    int digit = 0, num = n;
    while (num > 0) {
        digit++;
        num /= 10;
    }
    num = n;
    int i, j;
    for (i = 0, j = digit - 1; i < j; i++, j--) {
        if ((num / (int)pow(10, j)) % 10 != (num / (int)pow(10, i)) % 10) {
            return 0;
        }
    }
    return 1;
}

int main()
{
    int n, i;
    printf("Enter the value of n: ");
    scanf("%d", &n);

    printf("Palindrome prime numbers from 1 to %d: ", n);
    for (i = 2; i <= n; i++) {
        if (isPrime(i) && isPalindrome(i)) {
            printf("%d ", i);
        }
    }

    return 0;
}

9. 双向环形素数：

#include <stdio.h>
#include <math.h>

int isPrime(int n)
{
    int i;
    if (n == 2 || n == 3) {
        return 1;
    }
    if (n % 6 != 1 && n % 6 != 5) {
        return 0;
    }
    for (i = 2; i <= sqrt(n); i++) {
        if (n % i == 0) {
            return 0;
        }
    }
    return 1;
}

int isCircularPrime(int n)
{
    int num = n;
    int digit = 0;
    while (num > 0) {
        digit++;
        num /= 10;
    }
    num = n;
    int i, j;
    for (i = 0; i < digit; i++) {
        if (!isPrime(num)) {
            return 0;
        }
        int rem = num % 10;
        num = rem * pow(10, digit - 1) + num / 10;
    }
    return 1;
}

int main()
{
    int n, i;
    printf("Enter the value of n: ");
    scanf("%d", &n);

    printf("Circular prime numbers from 1 to %d: ", n);
    for (i = 2; i <= n; i++) {
        if (isCircularPrime(i)) {
            printf("%d ", i);
        }
    }

    return 0;
}

10. 菜单调用程序：

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

int isPrime(int n)
{
    int i;
    if (n == 2 || n == 3) {
        return 1;
    }
    if (n % 6 != 1 && n % 6 != 5) {
        return 0;
    }
    for (i = 2; i <= sqrt(n); i++) {
        if (n % i == 0) {
            return 0;
        }
    }
    return 1;
}

void sieveOfEratosthenes(int n)
{
    int primes[n + 1];
    memset(primes, 1, sizeof(primes));

    int i, j;
    for (i = 2; i * i <= n; i++) {
        if (primes[i]) {
            for (j = i * i; j <= n; j += i) {
                primes[j] = 0;
            }
        }
    }

    printf("Prime numbers from 1 to %d are: ", n);
    for (i = 2; i <= n; i++) {
        if (primes[i]) {
            printf("%d ", i);
        }
    }
}

void circularPrimes(int n)
{
    int num = n;
    int digit = 0;
    while (num > 0) {
        digit++;
        num /= 10;
    }
    num = n;
    int i, j;
    for (i = 0; i < digit; i++) {
        if (!isPrime(num)) {
            printf("%d is not a circular prime", n);
            return;
        }
        int rem = num % 10;
        num = rem * pow(10, digit - 1) + num / 10;
    }
    printf("%d is a circular prime", n);
}

int main()
{
    int choice, n;
    do {
        printf("\n1. Sieve of Eratosthenes\n2. Circular Primes\n3. Exit\nEnter your choice: ");
        scanf("%d", &choice);
        switch (choice) {
            case 1:
                printf("Enter the value of n: ");
                scanf("%d", &n);
                sieveOfEratosthenes(n);
                break;
            case 2:
                printf("Enter the value of n: ");
                scanf("%d", &n);
                circularPrimes(n);
                break;
            case 3:
                printf("Exiting program...");
                break;
            default:
                printf("Invalid choice, please try again.");
                break;
        }
    } while (choice != 3);

    return 0;
}