Problem:
Score : 400 points

Problem Statement

We say that a odd number N is similar to 2017 when both N and (N+1)/2 are prime.

You are given Q queries.

In the i-th query, given two odd numbers l_i and r_i, find the number of odd numbers x similar to 2017 such that l_i ≤ x ≤ r_i.

Constraints

1≤Q≤10^5

1≤l_i≤r_i≤10^5

l_i and r_i are odd.

All input values are integers.

Input

Input is given from Standard Input in the following format:

Q
l_1 r_1
:
l_Q r_Q

Output

Print Q lines. The i-th line (1≤i≤Q) should contain the response to the i-th query.

Sample Input 1

1
3 7

Sample Output 1

2

3 is similar to 2017, since both 3 and (3+1)/2=2 are prime.

5 is similar to 2017, since both 5 and (5+1)/2=3 are prime.

7 is not similar to 2017, since (7+1)/2=4 is not prime, although 7 is prime.

Thus, the response to the first query should be 2.

Sample Input 2

4
13 13
7 11
7 11
2017 2017

Sample Output 2

1
0
0
1

Note that 2017 is also similar to 2017.

Sample Input 3

6
1 53
13 91
37 55
19 51
73 91
13 49

Sample Output 3

4
4
1
1
1
2

Solution in C# (Mono-csc 3.5.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;

namespace Contest
{
  class Program
  {
    static void Main(string[] args)
    {
      ABC084.D();
    }
    class ABC084
    {
      public static void A()
      {
        Console.WriteLine(48 - Read.Int());
      }
      public static void B()
      {
        var A = Read.Int();
        var B = Read.Int();
        var S = Read.Str();
        if (S[A] != '-') { Console.WriteLine("No"); return; }
        for (int i = 0; i < A; ++i)
        {
          if (S[i] < '0' || '9' < S[i]) { Console.WriteLine("No"); return; }
        }
        for (int i = 0; i < B; ++i)
        {
          if (S[A + 1 + i] < '0' || '9' < S[A + 1 + i]) { Console.WriteLine("No"); return; }
        }
        Console.WriteLine("Yes");
      }
      public static void C()
      {
        var N = Read.Int();
        var CSF = Enumerable.Range(0, N - 1).Select(i => Read.IntN()).ToArray();
        var ans = new List<int>();
        for(int i = 0; i < N; ++i)
        {
          int t = 0;
          for(int j = i; j < N - 1; ++j)
          {
            var f = CSF[j][2];
            t = (Math.Max(t, CSF[j][1]) + f - 1) / f * f + CSF[j][0];
          }
          ans.Add(t);
        }
        Console.WriteLine(String.Join(Environment.NewLine, ans));
      }
      public static void D()
      {
        var Q = Read.Int();
        var LR = Read.TupleInt(Q);

        var primes = Util.GenPrimes(100000);
        var like2017 = new int[100001];
        for (int i = 3; i <= 100000; i += 1)
        {
          var isLike = primes.Contains(i) && primes.Contains((i + 1) / 2);
          like2017[i] = like2017[i - 1] + (isLike ? 1 : 0);
        }
        Console.WriteLine(String.Join(Environment.NewLine, LR.Select(x => like2017[x.Item2] - like2017[x.Item1 - 1])));
      }
    }


    class Util
    {
      public static T[,] Gen<T>(int r, int c, T v)
      {
        var matrix = new T[r, c];
        for (int i = 0; i < r; ++i)
        {
          for (int j = 0; j < c; ++j)
          {
            matrix[i, j] = v;
          }
        }
        return matrix;
      }
      public static long[] ASum(long[] array)
      {
        var res = new long[array.Length + 1];
        for (int i = 0; i < array.Length; ++i)
        {
          res[i + 1] = res[i] + array[i];
        }
        return res;
      }
      public static long[,] ASum(long[,] matrix)
      {
        var N = matrix.GetLength(0);
        var M = matrix.GetLength(1);
        var res = new long[N + 1, M + 1];
        for(int i = 0; i < N; ++i)
        {
          for(int j = 0; j < M; ++j)
          {
            res[i + 1, j + 1] = res[i, j + 1] + res[i + 1, j] - res[i, j] + matrix[i, j];
          }
        }
        return res;
      }
      public static Dictionary<T, long> Frequency<T>(T[] array)
      {
        var dict = new Dictionary<T, long>();
        foreach (var a in array)
        {
          if (!dict.ContainsKey(a)) { dict.Add(a, 0); }
          dict[a]++;
        }
        return dict;
      }
      public static bool IsPrime(long x)
      {
        var fact = Factorize(x);
        return fact.Count == 1 && fact.Values.ElementAt(0) == 1;
      }
      public static Dictionary<long, int> Factorize(long x)
      {
        var dict = new Dictionary<long, int>();
        long minp = 2;
        while (x > 1)
        {
          bool ok = false;
          for (long p = minp; p * p <= x; ++p)
          {
            if (x % p == 0)
            {
              if (!dict.ContainsKey(p))
              {
                dict.Add(p, 0);
              }
              dict[p]++;
              minp = p;
              x /= p;
              ok = true;
              break;
            }
          }
          if (!ok)
          {
            if (!dict.ContainsKey(x)) { dict.Add(x, 0); }
            dict[x]++;
            break;
          }
        }
        return dict;
      }
      public static HashSet<int> GenPrimes(int max)
      {
        var primes = new HashSet<int>(Enumerable.Range(2, max - 1));
        for(int i = 2; i <= max; ++i)
        {
          if (primes.Contains(i))
          {
            for(int j=2; ; ++j)
            {
              if (i * j > max) { break; }
              primes.Remove(i * j);
            }
          }
        }
        return primes;
      }
    }

    static class Read
{
static Queue<string> queue = new Queue<string>();
static void Enqueue() { var ss = Console.ReadLine().Split(' '); foreach (var s in ss) { queue.Enqueue(s); } }
public static int Int() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt32(queue.Dequeue()); }
public static long Long() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt64(queue.Dequeue()); }
public static string Str() { if (queue.Count == 0) { Enqueue(); } return queue.Dequeue(); }
public static int[] IntN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray(); }
public static long[] LongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray(); }
public static ulong[] ULongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToUInt64(s)).ToArray(); }
public static string[] StrN() { return Console.ReadLine().Split(' '); }
public static Tuple<int, int>[] TupleInt(int n) { List<Tuple<int, int>> list = new List<Tuple<int, int>>(); for (int i = 0; i < n; ++i) { var ab = Read.IntN(); list.Add(new Tuple<int, int>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<long, long>[] TupleLong(int n) { List<Tuple<long, long>> list = new List<Tuple<long, long>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<long, long>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<string, string>[] TupleStr(int n) { List<Tuple<string, string>> list = new List<Tuple<string, string>>(); for (int i = 0; i < n; ++i) { var ab = Read.StrN(); list.Add(new Tuple<string, string>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<double, double>[] TupleDouble(int n) { List<Tuple<double, double>> list = new List<Tuple<double, double>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<double, double>(ab[0], ab[1])); } return list.ToArray(); }
public static long[,] LongMatrix(int r, int c) { var mat = new long[r, c]; for (int i = 0; i < r; ++i) { var x = Read.LongN(); for (int j = 0; j < c; ++j) { mat[i, j] = x[j]; } } return mat; }
public static Dictionary<int, HashSet<int>> AdjacencyList(int N, int M, bool isDirectional = false)
{
Dictionary<int, HashSet<int>> dict = new Dictionary<int, HashSet<int>>();
for (int i = 0; i <= N; ++i) { dict.Add(i, new HashSet<int>()); }
        for (int i = 0; i < M; ++i) { var ab = Read.IntN(); if (!dict[ab[0]].Contains(ab[1])) { dict[ab[0]].Add(ab[1]); } if (!isDirectional && !dict[ab[1]].Contains(ab[0])) { dict[ab[1]].Add(ab[0]); } }
        return dict;
}
public static Dictionary<int, Dictionary<int, long>> AdjacencyListWithWeight(int N, int M)
{
Dictionary<int, Dictionary<int, long>> dict = new Dictionary<int, Dictionary<int, long>>(); for (int i = 0; i <= N; ++i) { dict.Add(i, new Dictionary<int, long>()); }
for (int i = 0; i < M; ++i) { var ab = Read.IntN(); dict[ab[0]].Add(ab[1], ab[2]); dict[ab[1]].Add(ab[0], ab[2]); }
return dict;
}
}
    }
}