查看“︁质数判断”︁的源代码

==判断单个质数==

<math>O(\sqrt{x})</math>

<syntaxhighlight lang="cpp" line>
bool is_prime(long long x)
{
    if (x < 2)
        return false;
    for (long long i = 2; i * i <= x; i++)
        if (x % i == 0)
            return false;
    return true;
}
</syntaxhighlight>

==筛法==

===埃氏筛===

<math>O(n\log \log n)</math>

<syntaxhighlight lang="cpp" line>
const int MAXN = 10'000'000;
bool p[MAXN + 1];
//筛出 1~n 中的每个数是否为质数
void get_primes(int n)
{
    //初始化
    p[0] = p[1] = false;
    for (int i = 2; i <= n; i++)
        p[i] = true;
    //筛
    for (int i = 2; i <= n; i++)
        if (p[i])
            for (int j = i + i; j <= n; j += i)
                p[j] = false;
}
</syntaxhighlight>

===线性筛/欧拉筛===

<math>O(n)</math>

<syntaxhighlight lang="cpp" line>
const int MAXN = 10'000'000;
bool p[MAXN + 1];
vector<int> pri;
// 筛出 1~n 中的每个数是否为质数
void get_primes(int n)
{
    for (int i = 1; i <= n; i++)
        p[i] = true;
    p[0] = p[1] = false;
    for (int i = 2; i <= n; i++)
    {
        if (p[i])
            pri.push_back(i);
        for (int j = 0; j < pri.size(); j++)
        {
            // i*pri[j]
            if (i * pri[j] > n)
                break;
            p[i * pri[j]] = false;
            if (i % pri[j] == 0)
                break;
        }
    }
}
</syntaxhighlight>