孪生素数

1.问题描述

所谓孪生素数指的是间隔为2的两个相邻素数，因为它们之间的距离已经近得不能再近了，如同孪生兄弟一样，所以将这一对素数称为孪生素数。编程求出10000以内的所有孪生素数。

2.源码实现

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

/*求平方根*/
int isqrt(int a)
{
    int i;

    if(a == 1)
    {
        return 1;
    }

    for(i=1; i<a; i++)
    {
        if(i*i > a)
        {
            break;
        }
    }

    return i-1;
}

/*判断是否为质数*/
short isPrime(int a)
{
    int u;
    int i;

    if(a == 1)
    {
        return 0;
    }

    u = isqrt(a);

    for(i=2; i<=u; i++)
    {
        if(a % i == 0)
        {
            return 0;
        }
    }

    return 1;
}

int main()
{
    int n = 10000;
    int i = 0;
    int j = 1;

    for(i=1; i<10000; i++)
    {
        if(isPrime(i) && isPrime(i+2))
        {
            if(j % 5 == 0)
            {
                printf("(%04d, %04d)\n", i, i+2);
            }
            else
            {
                printf("(%04d, %04d) ", i, i+2);
            }

            j++;
        }
    }

    if(j % 5 != 1)
    {
        printf("\n");
    }

    return 0;
}

3.编译源码

$ gcc -o test test.c -std=c89

4.运行及其结果

$ ./test
(0003, 0005) (0005, 0007) (0011, 0013) (0017, 0019) (0029, 0031)
(0041, 0043) (0059, 0061) (0071, 0073) (0101, 0103) (0107, 0109)
(0137, 0139) (0149, 0151) (0179, 0181) (0191, 0193) (0197, 0199)
(0227, 0229) (0239, 0241) (0269, 0271) (0281, 0283) (0311, 0313)
(0347, 0349) (0419, 0421) (0431, 0433) (0461, 0463) (0521, 0523)
(0569, 0571) (0599, 0601) (0617, 0619) (0641, 0643) (0659, 0661)
(0809, 0811) (0821, 0823) (0827, 0829) (0857, 0859) (0881, 0883)
(1019, 1021) (1031, 1033) (1049, 1051) (1061, 1063) (1091, 1093)
(1151, 1153) (1229, 1231) (1277, 1279) (1289, 1291) (1301, 1303)
(1319, 1321) (1427, 1429) (1451, 1453) (1481, 1483) (1487, 1489)
(1607, 1609) (1619, 1621) (1667, 1669) (1697, 1699) (1721, 1723)
(1787, 1789) (1871, 1873) (1877, 1879) (1931, 1933) (1949, 1951)
(1997, 1999) (2027, 2029) (2081, 2083) (2087, 2089) (2111, 2113)
(2129, 2131) (2141, 2143) (2237, 2239) (2267, 2269) (2309, 2311)
(2339, 2341) (2381, 2383) (2549, 2551) (2591, 2593) (2657, 2659)
(2687, 2689) (2711, 2713) (2729, 2731) (2789, 2791) (2801, 2803)
(2969, 2971) (2999, 3001) (3119, 3121) (3167, 3169) (3251, 3253)
(3257, 3259) (3299, 3301) (3329, 3331) (3359, 3361) (3371, 3373)
(3389, 3391) (3461, 3463) (3467, 3469) (3527, 3529) (3539, 3541)
(3557, 3559) (3581, 3583) (3671, 3673) (3767, 3769) (3821, 3823)
(3851, 3853) (3917, 3919) (3929, 3931) (4001, 4003) (4019, 4021)
(4049, 4051) (4091, 4093) (4127, 4129) (4157, 4159) (4217, 4219)
(4229, 4231) (4241, 4243) (4259, 4261) (4271, 4273) (4337, 4339)
(4421, 4423) (4481, 4483) (4517, 4519) (4547, 4549) (4637, 4639)
(4649, 4651) (4721, 4723) (4787, 4789) (4799, 4801) (4931, 4933)
(4967, 4969) (5009, 5011) (5021, 5023) (5099, 5101) (5231, 5233)
(5279, 5281) (5417, 5419) (5441, 5443) (5477, 5479) (5501, 5503)
(5519, 5521) (5639, 5641) (5651, 5653) (5657, 5659) (5741, 5743)
(5849, 5851) (5867, 5869) (5879, 5881) (6089, 6091) (6131, 6133)
(6197, 6199) (6269, 6271) (6299, 6301) (6359, 6361) (6449, 6451)
(6551, 6553) (6569, 6571) (6659, 6661) (6689, 6691) (6701, 6703)
(6761, 6763) (6779, 6781) (6791, 6793) (6827, 6829) (6869, 6871)
(6947, 6949) (6959, 6961) (7127, 7129) (7211, 7213) (7307, 7309)
(7331, 7333) (7349, 7351) (7457, 7459) (7487, 7489) (7547, 7549)
(7559, 7561) (7589, 7591) (7757, 7759) (7877, 7879) (7949, 7951)
(8009, 8011) (8087, 8089) (8219, 8221) (8231, 8233) (8291, 8293)
(8387, 8389) (8429, 8431) (8537, 8539) (8597, 8599) (8627, 8629)
(8819, 8821) (8837, 8839) (8861, 8863) (8969, 8971) (8999, 9001)
(9011, 9013) (9041, 9043) (9239, 9241) (9281, 9283) (9341, 9343)
(9419, 9421) (9431, 9433) (9437, 9439) (9461, 9463) (9629, 9631)
(9677, 9679) (9719, 9721) (9767, 9769) (9857, 9859) (9929, 9931)