using System; using System.Text; using CompLib.Mathematics; public class Program { public void Solve() { var sc = new Scanner(); int q = sc.NextInt(); var sb = new StringBuilder(); for (int i = 0; i < q; i++) { sb.AppendLine(Query(sc.NextLong())); } Console.Write(sb.ToString()); } string Query(long n) { // Goldbach's conjecture // n <= 10^18では真 if (n % 2 == 0) { return n == 2 ? "No" : "Yes"; } // nは奇数 // p,qが奇素数ならnは偶数になるはず // どちらかは2 // 対称性より p = 2とする if (n < 5) return "No"; for (long pa = 2; pa < n; pa *= 2) { long qb = n - pa; for (long b = 1; b <= 60; b++) { long min = 0; long max = (long) Math.Pow(long.MaxValue, (double) 1 / b); while (max - min > 1) { long med = (max + min) / 2; if (Pow(med, b) <= qb) { min = med; } else { max = med; } } if (min < 2) break; if (Pow(min, b) == qb && PrimalityTest.IsPrime(min)) { return "Yes"; } } } return "No"; } public long Pow(long a, long b) { if (b == 0) return 1; long res = Pow(a * a, b / 2); if (b % 2 == 1) res *= a; return res; } public static void Main(string[] args) { new Program().Solve(); } } namespace CompLib.Mathematics { using System; public static class PrimalityTest { private static Random Random = new Random(); /// /// Miller-Rabin素数判定法を用いてnが素数か判定 O(k log^2 n) /// /// /// /// public static bool IsPrime(long n, int k = 60) { if (n < 2) return false; if (n == 2) return true; if (n % 2 == 0) return false; if (n < 10000) { for (int i = 3; i * i <= n; i++) { if (n % i == 0) { return false; } } return true; } if (!StrongFermatTest(2, n)) { return false; } for (int i = 0; i < k; i++) { if (!StrongFermatTest(NextLong(2, n), n)) { return false; } } return true; } public static bool StrongFermatTest(long a, long n) { long t = n - 1; long t2 = t; while (t % 2 == 0) { t /= 2; if (Pow(a, t, n) == t2) { return true; } } return Pow(a, t, n) == 1; } private static long Pow(long x, long y, long mod) { x %= mod; long result = 1; while (y > 0) { if (y % 2 == 1) { result = Multiplication(result, x, mod); } x = Multiplication(x, x, mod); y /= 2; } return result; } private static long Multiplication(long a, long b, long mod) { if (mod < int.MaxValue) { return (a * b) % mod; } long result = 0; while (b > 0) { if (b % 2 == 1) { result += a; result %= mod; } a *= 2; a %= mod; b /= 2; } return result; } private static long NextLong(long min, long max) { long d = max - min; long result = Random.Next(); result <<= 31; result += Random.Next(); result %= d; return result + min; } } } class Scanner { public Scanner() { _pos = 0; _line = new string[0]; } const char Separator = ' '; private int _pos; private string[] _line; #region スペース区切りで取得 public string Next() { if (_pos >= _line.Length) { _line = Console.ReadLine().Split(Separator); _pos = 0; } return _line[_pos++]; } public int NextInt() { return int.Parse(Next()); } public long NextLong() { return long.Parse(Next()); } public double NextDouble() { return double.Parse(Next()); } #endregion #region 型変換 private int[] ToIntArray(string[] array) { var result = new int[array.Length]; for (int i = 0; i < array.Length; i++) { result[i] = int.Parse(array[i]); } return result; } private long[] ToLongArray(string[] array) { var result = new long[array.Length]; for (int i = 0; i < array.Length; i++) { result[i] = long.Parse(array[i]); } return result; } private double[] ToDoubleArray(string[] array) { var result = new double[array.Length]; for (int i = 0; i < array.Length; i++) { result[i] = double.Parse(array[i]); } return result; } #endregion #region 配列取得 public string[] Array() { if (_pos >= _line.Length) _line = Console.ReadLine().Split(Separator); _pos = _line.Length; return _line; } public int[] IntArray() { return ToIntArray(Array()); } public long[] LongArray() { return ToLongArray(Array()); } public double[] DoubleArray() { return ToDoubleArray(Array()); } #endregion }