用C++实现的Eratosthenes筛法程序

运行示例

只输出素数总数的运行示例

PS H:\Read\num\x64\Release> .\esieve.exe

Eratosthenes sieve: a method to find out all primes below the number that you specify here please: 1234567

Only the sum of all primes needed [y/n](y as default):

Start to work out the sum of all primes below 1234567...
95360 primes found in 15 milliseconds.

PS H:\Read\num\x64\Release> .\esieve.exe
Eratosthenes sieve: a method to find out all primes below the number that you specify here please: 12345678

Only the sum of all primes needed [y/n](y as default):

Start to work out the sum of all primes below 12345678...
809227 primes found in 203 milliseconds.

PS H:\Read\num\x64\Release> .\esieve.exe
Eratosthenes sieve: a method to find out all primes below the number that you specify here please: 123456789

Only the sum of all primes needed [y/n](y as default):

Start to work out the sum of all primes below 123456789...
7027260 primes found in 2219 milliseconds.

PS H:\Read\num\x64\Release> .\esieve.exe
Eratosthenes sieve: a method to find out all primes below the number that you specify here please: 1234567890

Only the sum of all primes needed [y/n](y as default):

Start to work out the sum of all primes below 1234567890...
62106578 primes found in 28297 milliseconds.

PS H:\Read\num\x64\Release>

从上面的示例结果看，用Eratosthenes筛法实现的程序从1到1234567，百万级的总数中，求出全体素数只用了大约15毫秒；随后的从千万级、亿级、十亿级总数中求出全体素数花费的时间分别大约为203毫秒、2秒219毫秒、28秒297毫秒。

输出素数清单的运行示例

PS H:\Read\num\x64\Release> .\esieve.exe

Eratosthenes sieve: a method to find out all primes below the number that you specify here please: 100

Only the sum of all primes needed [y/n](y as default): n

Start to work out all primes below 100...
25 primes found in 0 milliseconds.

2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97
PS H:\Read\num\x64\Release> .\esieve.exe

Eratosthenes sieve: a method to find out all primes below the number that you specify here please: 123456

Only the sum of all primes needed [y/n](y as default): n

Start to work out all primes below 123456...
11601 primes found in 0 milliseconds.

2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,
547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,1193,1201,1213,1217,1223,
1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,1601,1607,1609,1613,1619,1621,1627,1637,1657,1663,1667,1669,1693,1697,1699,1709,1721,1723,1733,1741,1747,1753,1759,1777,1783,1787,1789,1801,1811,1823,1831,1847,1861,1867,1871,1873,1877,1879,1889,1901,1907,1913,1931,1933,1949,1951,1973,1979,1987,
1993,1997,1999,2003,2011,2017,2027,2029,2039,2053,2063,2069,2081,2083,2087,2089,2099,2111,2113,2129,2131,2137,2141,2143,2153,2161,2179,2203,2207,2213,2221,2237,2239,2243,2251,2267,2269,2273,2281,2287,2293,2297,2309,2311,2333,2339,2341,2347,2351,2357,2371,2377,2381,2383,2389,2393,2399,2411,2417,2423,2437,2441,2447,2459,2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,2557,2579,2591,2593,2609,2617,2621,2633,2647,2657,2659,2663,2671,2677,2683,2687,2689,2693,2699,2707,2711,2713,2719,2729,2731,2741,
2749,2753,2767,2777,2789,2791,2797,2801,2803,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897,2903,2909,2917,2927,2939,2953,2957,2963,2969,2971,2999,3001,3011,3019,3023,3037,3041,3049,3061,3067,3079,3083,3089,3109,3119,3121,3137,3163,3167,3169,3181,3187,3191,3203,3209,3217,3221,3229,3251,3253,3257,3259,3271,3299,3301,3307,3313,3319,3323,3329,3331,3343,3347,3359,3361,3371,3373,3389,3391,3407,3413,3433,3449,3457,3461,3463,3467,3469,3491,3499,3511,3517,3527,3529,3533,3539,3541,3547,3557,3559,3571,
500 primes listed, 11101 left to show [c] continue; <q> quit: q

PS H:\Read\num\x64\Release>

Eratosthenes筛法的C++程序实现

宏定义和全局量定义

1 typedef unsigned char u8;
2 typedef unsigned long ulong;
3 static ulong s_last = 0;
4 static u8* s_pAll = NULL;
5 static std::vector<ulong> s_vecPrime;

renewCurrentPrime函数实现

1 bool renewCurrentPrime(ulong& prime)
2 {
3     while (prime < s_last) {
4         ++prime;
5         if (s_pAll[prime - 1] == 1)
6             return true;
7     }
8     return false;
9 }

showDetails函数实现

 1 void showDetails()
 2 {
 3     ulong pos = 0;
 4     while (true) {
 5         if (pos >= s_vecPrime.size())
 6             break;
 7         std::cout << s_vecPrime[pos++];
 8         if (pos < s_vecPrime.size())
 9             std::cout << ",";
10         if (pos % 500 == 0) {
11             printf("\n %u primes listed, %u left to show [c] continue; <q> quit: ", pos, s_vecPrime.size() - pos);
12             std::string strInput;
13             getline(std::cin, strInput);
14             if (strInput == "q")
15                 break;
16             std::cout << std::endl;
17         }
18         if (pos % 100 == 0)
19             std::cout << std::endl;
20     }
21 }

main函数实现

 1 int main()
 2 {
 3     printf(" Eratosthenes sieve: a method to find out all primes below the number that you specify here please: ");
 4     std::string strInput;
 5     getline(std::cin, strInput);
 6     s_last = strtoul(strInput.c_str(), 0, 10);
 7     if (s_last <= 2) {
 8         printf("\n Wrong input.\n");
 9         return 0;
10     }
11     printf("\n Only the sum of all primes needed [y/n](y as default): ");
12     getline(std::cin, strInput);
13     bool bDetail = (strInput == "n");
14     if (bDetail)
15         printf("\n Start to work out all primes below %u...\n", s_last);
16     else
17         printf("\n Start to work out the sum of all primes below %u...\n", s_last);
18     DWORD tickBegin = GetTickCount();
19     s_pAll = new u8[s_last];
20     if (!s_pAll) {
21         printf("Lack of memory.\n");
22         return 0;
23     }
24
25     ulong sum = 0;
26     ulong curPrime = 1;
27     memset(s_pAll, 1, s_last);
28     s_pAll[0] = 0; // set 1 non-prime
29     while (true) {
30         renewCurrentPrime(curPrime);
31         ++sum;
32         if (bDetail)
33             s_vecPrime.push_back(curPrime);
34         if (curPrime * curPrime > s_last)
35             break;
36         for (int idx = curPrime - 1; idx <= s_last - 1; idx += curPrime) {
37             s_pAll[idx] = 0;
38         }
39     }
40     /// pick up all the left primes
41     for (int idx = curPrime; idx < s_last; ++idx) {
42         if (s_pAll[idx] == 1) {
43             ++sum;
44             if (bDetail)
45                 s_vecPrime.push_back(idx + 1);
46         }
47     }
48     printf(" %u primes found in %u milliseconds.\n\n", sum, GetTickCount() - tickBegin);
49     delete []s_pAll;
50     if (bDetail)
51         showDetails();
52     return 0;
53 }

其他

https://github.com/readalps/EratosthenesSieve上放了源码文件，以及两个运行结果文件，其中all primes below 123456.txt里列出了1到123456范围内的全体素数。