二分+阶乘(看质因数的个数是否够)
详细看大佬的博客：
https://blog.nowcoder.net/n/aa5ff9efa80440c897a9aaae4401a467?f=comment

#include<iostream>
#include<math.h>
#include<cstring>
using namespace std;
typedef long long ll;
const int maxn=1e5+1; 
int num[maxn];
int sum[maxn];
ll k;
bool judge(ll x){
    for(int i=1;i<=k;i++){
        ll n=x,sm=0;
        while(n){
            sm+=n/num[i];
            n/=num[i];
        }
        if(sm<sum[i])return false;
    }return true;
}
int main(){
    int t;ll p;
    cin>>t;
    while(t--){
        cin>>p;
        memset(sum,0,sizeof sum);
        k=0;
        ll tp=p;
        for(int i=2;i*i<=tp;i++){
            if(tp%i==0){
                num[++k]=i;
                while(tp%i==0){
                    sum[k]++;
                    tp/=i;
                }    
            }
        }if(tp!=1){
            num[++k]=tp;
            sum[k]++;
        }
//        for(int i=1;i<=k;i++){
//            cout<<num[i]<<" "<<sum[i]<<endl;
//        }
        ll l=1,r=p;
        while(l<=r){
            ll mid=(l+r)>>1;
            //cout<<mid<<" "<<l<<" "<<r<<endl;
            if(judge(mid)){
                r=mid-1;
            }else{
                l=mid+1;
            }
        }cout<<r+1<<endl;
    }
    return 0;
}