using System; using System.IO; using System.Collections.Generic; using System.Linq; using System.Numerics; namespace No3030 { public class Program { void Solve(StreamScanner ss, StreamWriter sw) { //--------------------------------- var N = ss.Next(int.Parse); for (var i = 0; i < N; i++) { var X = ss.Next(BigInteger.Parse); sw.WriteLine($"{X} {Convert.ToInt32(MillerRabin.IsPrime(X))}"); } //--------------------------------- } static void Main() { var ss = new StreamScanner(new StreamReader(Console.OpenStandardInput())); var sw = new StreamWriter(Console.OpenStandardOutput()) {AutoFlush = false}; new Program().Solve(ss, sw); sw.Flush(); } } public static class MillerRabin { const int RandomTestCount = 30; static readonly BigInteger[] BasePrimes = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41,}; static readonly BigInteger[] WitnessRanges = { 2047, 1373653, 25326001, 118670087467, //3215031751が例外 2152302898747, 3474749660383, 341550071728321, 341550071728321, 3825123056546413051, 3825123056546413051, 3825123056546413051, BigInteger.Parse("318665857834031151167461"), BigInteger.Parse("3317044064679887385961981"), }; public static bool IsPrime(BigInteger n) { if (n < 2 || n == 3215031751) return false; if (n < 42) return BasePrimes.Contains(n); if (BasePrimes.Any(p => n % p == 0)) return false; var d = n - 1; while ((d & 1) == 0) d >>= 1; for (var i = 0; i < BasePrimes.Length; i++) { if (!MillerRabinTest(n, d, BasePrimes[i])) return false; if (n < WitnessRanges[i]) return true; } //n > 3.3e24 var random = new Random(); for (var i = 0; i < RandomTestCount; i++) { if (!MillerRabinTest(n, d, random.Next(1, int.MaxValue))) return false; } return true; } static bool MillerRabinTest(BigInteger n, BigInteger d, BigInteger a) { a = BigInteger.ModPow(a, d, n); if (a == 1 || a == n - 1) return true; while ((d <<= 1) < n - 1) { a = a * a % n; if (a == n - 1) return true; } return false; } } public class StreamScanner { static readonly char[] Sep = {' '}; readonly Queue buffer = new Queue(); readonly TextReader textReader; public StreamScanner(TextReader textReader) { this.textReader = textReader; } public T Next(Func parser) { if (buffer.Count != 0) return parser(buffer.Dequeue()); var nextStrings = textReader.ReadLine().Split(Sep, StringSplitOptions.RemoveEmptyEntries); foreach (var nextString in nextStrings) buffer.Enqueue(nextString); return Next(parser); } public T[] Next(Func parser, int x) { var ret = new T[x]; for (var i = 0; i < x; ++i) ret[i] = Next(parser); return ret; } public T[][] Next(Func parser, int x, int y) { var ret = new T[y][]; for (var i = 0; i < y; ++i) ret[i] = Next(parser, x); return ret; } } }