线性筛素数模板（3种方法）

1朴素方法

#include <bits/stdc++.h>
#define maxn 200005
typedef long long ll;
using namespace std;
int prime(int n)
{
    if(n < 2)return 0;
    for(int i = 2; i * i <= n; i ++)
    if(n%i == 0)
    return 0;
    return 1;
}
int main()
{
    ios::sync_with_stdio(0);
    cin.tie(0),cout.tie(0);
    ll n,m;
    cin >> n >> m;
    while(m--)
    {
        ll x;
        cin >> x;
        if(prime(x))cout << "Yes" << endl;
        else cout << "No" << endl;
    }
    return 0;
}

2 筛除倍数，一个素数的倍数一定不是素数；

#include <bits/stdc++.h>
#define maxn 10000005
typedef long long ll;
using namespace std;
bool a[maxn];
ll n,m;
void prime()
{
    memset(a,1,sizeof(a));
    a[1] = a[0] = 0;
    for(int i = 2; i <= n; i ++)
    {
        if(a[i] == 1)
        {
            for(int j = 2; j * i <= n; j ++)
            {
                a[i*j] = 0;
            }
        }
    }
}
int main()
{
    cin >> n >> m;
    prime();
    while(m--)
    {
        ll x;
        cin >> x;
        if(a[x])
            cout << "Yes" << endl;
        else
            cout << "No" << endl;
    }
    return 0;
}

3一个大于5的素数一定在6的倍数周围

#include <bits/stdc++.h>
#define maxn 10000005
typedef long long ll;
using namespace std;
ll n,m;
int prime(int n)
{
    if(n < 2)return 0;
    if(n ==2 || n == 3)return 1;
    if(n % 6 != 1 && n % 6 != 5)return 0;
    for(int i = 5; i * i <= n; i += 6)
    {
        if(n % i == 0 || n % (i + 2) == 0)
        return 0;
    }
    return 1;
}
int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0),cout.tie(0);
    cin >> n >> m;
    while(m--)
    {
        ll x;
        cin >> x;
        if(prime(x))
            cout << "Yes" << endl;
        else
            cout << "No" << endl;
    }
    return 0;
}