题面

题解

太神仙了学不来orz

//minamoto#include
    
     #define R register#define ll long long#define dd long double#define fp(i,a,b) for(int i=a,I=b+1;i
     
      I;--i)#define go(u) for(int i=head[u],v=e[i].v;i;i=e[i].nx,v=e[i].v)using namespace std;const int base[]={2,3,7,61,24251};inline ll mul(R ll x,R ll y,R ll P){R ll k=(dd)x*y/P;k=x*y-k*P;return k<0?k+P:k;}ll gcd(ll x,ll y){return y?gcd(y,x%y):x;}inline ll g(R ll x,R ll n,R ll c){x=mul(x,x,n)+c;return x>n?x-n:x;}inline ll Abs(R ll x){return x<0?-x:x;}ll ksm(R ll x,R ll y,R ll P){    R ll res=1;    for(;y;y>>=1,x=mul(x,x,P))if(y&1)res=mul(res,x,P);    return res;}bool miller(ll x){    if(x<2||x==46856248255981ll)return false;    if(x==2||x==3||x==7||x==61||x==24251)return true;    if(!(x&1)||!(x%3)||!(x%61)||!(x%24251))return false;    ll p=x-1;int t=0,j;    while(!(p&1))p>>=1,++t;    fp(i,0,4){        if(base[i]>x)break;        ll res=ksm(base[i],p,x);        if(res==1||res==x-1)continue;        for(j=1;j<=t;++j){            res=mul(res,res,x);            if(res==x-1)break;        }        if(j>t)return false;    }    return true;}const int M=(1<<7)-1;ll rho(ll n){    if(!(n&1))return 2;if(!(n%3))return 3;    ll x=0,y=x,t=1,q=1,c=rand()%(n-1)+1;    for(R int k=2;;k<<=1,y=x,q=1){        fp(i,1,k){            x=g(x,n,c);            q=mul(q,Abs(x-y),n);            if(!(i&M)){                t=gcd(q,n);                if(t>1)break;            }        }        if(t>1||(t=gcd(q,n))>1)break;    }    return t;}ll res;void find(ll x){    if(x==1||x<=res)return;    if(miller(x))return res=x,void();    ll p=x;    while(p==x)p=rho(x);    while(x%p==0)x/=p;    find(p),find(x);}int main(){    srand(time(0));//  freopen("testdata.in","r",stdin);    int T;ll n;scanf("%d",&T);    while(T--){        scanf("%lld",&n),res=0,find(n);        res==n?printf("Prime\n"):printf("%d\n",res);    }    return 0;}