## Editorial for Lại là số nguyên tố

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Lưu ý: Các code mẫu dưới đây chỉ mang tính tham khảo và có thể không AC được bài tập này

#### Code mẫu của flashmt

#include <iostream>
#include <algorithm>
#include <cstdio>
using namespace std;

unsigned long long power(unsigned long long x,unsigned long long y,unsigned long long z)
{
if (!y) return 1;
unsigned long long r=power(x,y/2,z);
r=r*r%z;
if (y%2) r=r*x%z;
return r;
}

int probablyPrime(unsigned long long n,int iteration)
{
if (n<3) return n==2;
if (n%2==0) return 0;

unsigned long long s=n-1,p=0;
while (s%2==0) s/=2, p++;

while (iteration--)
{
unsigned long long x=power(rand()%(n-1)+1,s,n);

for (int i=1;i<=p;i++)
{
unsigned long long xx=x;
x=x*x%n;
if (x==1 && xx!=1 && xx!=n-1) return 0;
}

if (x!=1) return 0;
}

return 1;
}

int main()
{
int test;
cin >> test;
while (test--)
{
unsigned long long n;
cin >> n;
n--;
while (!probablyPrime(n,10)) n--;
cout << n << endl;
}
}


#### Code mẫu của happyboy99x

#include <algorithm>
#include <bitset>
#include <cctype>
#include <cfloat>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <functional>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>
using namespace std;

typedef pair<int, int> ii;
typedef vector<ii> vii;
typedef vector<vii> vvii;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef unsigned long long LL;

#define sz(a) (int((a).size()))
#define fi first
#define se second
#define pb push_back
#define mp make_pair
#define all(c) (c).begin(), (c).end()
#define tr(c,i) for(typeof((c).begin()) i = (c).begin(), _e = (c).end(); i != _e; ++i)
#define present(c,x) ((c).find(x) != (c).end())
#define cpresent(c,x) (find(all(c),x) != (c).end())
#define rep(i,n) for(int i = 0, _n = (n); i < _n; ++i)
#define repd(i,n) for(int i = (n)-1; i >= 0; --i )
#define fo(i,a,b) for(int i = (a), _b = (b); i <= _b; ++i)
#define fod(i,a,b) for(int i = (a), _b = (b); i >= _b; --i)

#define INF 1000000000
#define N

LL powmod(LL a, LL b, LL n) {
if(b == 0) return 1;
LL res = powmod(a, b/2, n);
return (b%2==1) ? (((res*res)%n)*a)%n : ((res*res)%n);
}

bool MillerTest(LL n, LL s, LL m) {
LL a = (LL) rand() % (n-2) + 2, b = powmod(a, m, n);
LL pre = n-1;
repd(i,s+1) {
if(b == 1) return pre == n-1;
pre = b; b = (b*b) % n;
}
return 0;
}

bool prime(LL n) {
if(n == 2) return 1;
if(n % 2 == 0 || n < 2) return 0;
LL s = 63 - __builtin_clzll((n-1)&(1-n)), m = (n-1) >> s;
for(int k=0; k<30; ++k)
if(!MillerTest(n, s, m)) return 0;
return 1;
}

int main() {
#ifndef ONLINE_JUDGE
freopen( "input.txt", "r", stdin );
//freopen( "output.txt", "w", stdout );
#endif
int tc; LL n; srand(time(NULL));
scanf("%d",&tc);
while(tc--) {
scanf("%llu",&n);
while(!prime(--n));
printf("%llu\n", n);
}
return 0;
}


const   fi='';

function powmod(i,j,k:longword):qword;
var     t:qword;
begin
if j=1 then exit(i mod k);
t:=powmod(i,j div 2,k) mod k;
if odd(j) then
exit((((t*i) mod k)*t) mod k);
exit((t*t) mod k);
end;

function rabinmiller(p:longword):boolean;
var     temp,s,a:int64;
modul:qword;
i:longint;
begin

if (p<2) then exit(false);
if (p <> 2) and (p mod 2 = 0) then exit(false);
s:=p-1;
while s mod 2 = 0 do s:=s div 2;
for i:=1 to 3 do
begin
a:=random(p-3)+2;
temp:=s;
modul:=powmod(a,temp,p);
while (temp<>p-1) and (modul<>1) and (modul<>p-1) do
begin
modul:=((modul mod p)*(modul mod p)) mod p;
temp:=temp*2;
end;
if (modul<>p-1) and (temp mod 2 = 0) then exit(false);
end;
exit(true);
end;

procedure input;
var     i,t:longint;
j:int64;
inp:text;
begin
randomize;
assign(inp,fi);
reset(inp);
for i:=1 to t do
begin
dec(j);
while j>=2 do
begin
if rabinmiller(j) then
begin
writeln(j);
break;
end;
dec(j);
end;

end;
close(inp);
end;
begin
input;
end.


#### Code mẫu của RR

{$R+,Q+} {$Mode objFPC}
const
FINP          =       '';
FOUT          =       '';
k             =       2;
var
f1,f2         :       text;
n             :       qword;
test          :       longint;

procedure openF;
begin
assign(f1,FINP); reset(f1);
assign(f2,FOUT); rewrite(f2);
end;
procedure closeF;
begin
close(f1);
close(f2);
end;
//Miller-rabin test by Pham Quang Vu

//power = (a^q) mod n
function power(a,q,n:qword):qword; inline;
var
u:qword;
begin
if q=1 then exit(a mod n);
if q=0 then exit(1);
u:=power(a,q shr 1,n);
if q and 1=1 then exit( ((u*u) mod n*a) mod n )
else exit( (u*u) mod n );
end;
function millertest(n,a,q,t:qword):boolean; inline;
var
pre,c:qword;
i:longint;
begin
c:=power(a,q,n);
pre:=n-1;
for i:=0 to t do
begin
if c=1 then exit(pre=n-1);
pre:=c;
c:=(c*c) mod n;
end;
exit(false);
end;
//n = 2^t * q
procedure cal(n:qword; var q,t:qword); inline;
begin
t:=0;
while n and 1=0 do
begin
inc(t);
n:=n shr 1;
end;
q:=n;
end;
function prime(n:qword):boolean; inline;
var
i:longint;
a,q,t:qword;
begin
cal(n-1,q,t);
for i:=1 to k do
begin
a:=random(n-1)+1;
if not millertest(n,a,q,t) then exit(false);
end;
exit(true);
end;

//End of Miller-rabin test by Pham Quang Vu

procedure solve;
begin
n-=1;
if n and 1=0 then n-=1;
repeat
if (n=3) or (n=5) or (n=7) then
begin
writeln(f2,n);
exit;
end;
if (n mod 5>0) and (n mod 7>0) then
if (n mod 3>0) and prime(n) then
begin
writeln(f2,n);
exit;
end;
n-=2;
until false;
end;

begin
openF;
for test:=1 to test do
begin
if n=3 then writeln(f2,2)
else solve;
end;
closeF;
end.


#### Code mẫu của hieult

#include <stdio.h>
//#include <conio.h>
#include <stdlib.h>
#include <math.h>
#include <algorithm>

bool isPrime(int n) {
if (n<2) return false; // optional
for (int i=2; i*i<=n; ++i) if (n%i==0) return false;
return true;
}

unsigned long long power(unsigned long long a, unsigned long long d,unsigned long long n)
{
if(d==1) return a%n;
else
{
unsigned long long k = power(a,d/2,n);
if(d%2==0) return k*k%n;
else return ((k*k)%n*a)%n;
}
}
bool rabinMiller(unsigned long long n, int k) {
if (n<=50) return isPrime(n);
unsigned long long d=n-1, s=0;
while (d%2==0) {++s; d/=2;}
for (int i=1; i<=k; ++i) {
unsigned long long a = rand()%(n-2)+2;
unsigned long long x = power(a,d,n);
if (x == 1 || x == n-1) continue;
for (int r=1; r<s; ++r) {
x=(unsigned long long)(x*x) % n;
if (x==1) return false;
if (x==n-1) break;
}
if (x!=n-1) return false;
}
return true;
}

int main()
{
int test;
unsigned long long n;
scanf("%d",&test);
for(int i = 1;i<=test;i++)
{
scanf("%lld",&n);
n--;
while(true)
{
if(rabinMiller(n,20))
{
printf("%lld\n",n);
break;
}
n--;
}
}
// getch();
}


#### Code mẫu của ll931110

{\$MODE DELPHI}
Program PAGAIN;
Const
input  = '';
output = '';
a: array[1..3] of integer = (2,7,61);
Var
i,t: integer;
n: qword;
fi,fo: text;

Procedure openfile;
Begin
Assign(fi, input);
Reset(fi);

Assign(fo, output);
Rewrite(fo);
End;

Function power(x,p,k: qword): qword;
Var
u: qword;
Begin
If p = 0 then exit(1);

u:= power(x,p div 2,k);
If odd(p) then power:= ((u * u) mod k * x) mod k
else power:= (u * u) mod k;
End;

Function RabinMiller(k: qword): boolean;
Var
i,j: integer;
st,test,bs,p2: qword;
ch: boolean;
Begin
bs:= k - 1;
p2:= 0;
While bs mod 2 = 0 do
Begin
bs:= bs div 2;
inc(p2);
End;

RabinMiller:= false;
ch:= true;

For i:= 1 to 3 do if k >= a[i] then
Begin
ch:= false;
st:= power(a[i],bs,k);

test:= st;
If (test = 1) or (test = k - 1) then
Begin
ch:= true;
break;
End;

For j:= 1 to p2 - 1 do
Begin
test:= (test * test) mod k;
If (test = 1) or (test = k - 1) then
Begin
ch:= true;
break;
End;
End;

If not ch then exit(false);
End;

RabinMiller:= true;
End;

Procedure solve;
Var
k: qword;
Begin
If n = 3 then
Begin
writeln(fo, 2);
exit;
End;

k:= n;
dec(k);
If not odd(k) then dec(k);

While not RabinMiller(k) do k:= k - 2;
Writeln(fo, k);
End;

Procedure closefile;
Begin
Close(fo);
Close(fi);
End;

Begin
openfile;