Factorial Factors (UVa) - Less Complexity

#include <bits/stdc++.h>
using namespace std;
const int M = 1 << 16;

vector<int> primes;

void sieve()
{
    vector<bool> comp(M + 5, 0);
    for (int i = 2; i * i <= M; i++)
    {
        if (!comp[i])
        {
            for (int j = i * i; j <= M; j += i)
            {
                comp[j] = 1;
            }
        }
    }
    primes.clear();
    primes = {2};
    for (int i = 3; i <= M; i += 2)
    {
        if (!comp[i])
        {
            primes.push_back(i);
        }
    }
}

bool is_prime(long long n)
{
    for (int i = 0; i < primes.size() && primes[i] * primes[i] <= n; i++)
    {
        if (n % primes[i] == 0)
        {
            return false;
        }
    }
    return true;
}

int main()
{
    sieve();
    int T;
    scanf("%d", &T);
    while (T--)
    {
        long long n;
        scanf("%lld", &n);
        for (auto i = n - 1; i > 1; i--)
        {
            if (is_prime(i))
            {
                printf("%lld\n", i);
                break;
            }
        }
    }
    return 0;
}