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 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Runtime.CompilerServices;
using System.Text;
using System.Threading.Tasks;

namespace AtCorder
{
	public class Program
	{
		static void Main(string[] args)
		{
			var cin = new Scanner2();
			int q = cin.Int();
			int n = 100000;

			var sieve = new Sieve(n);
			var rui = new int[n + 1];
			for (int i = 0; i < n; i++) {
				rui[i + 1] = rui[i] + (sieve.IsPrime(i + 1) && sieve.IsPrime((i + 2) / 2) ? 1 : 0);
			}

			var sb = new StringBuilder();
			for (int i = 0; i < q; i++) {
				int l = cin.Int() - 1;
				int r = cin.Int();
				sb.AppendLine((rui[r] - rui[l]).ToString());
			}

			Console.Write(sb.ToString());
		}
	}

	public class Sieve
	{
		private List<long> primes_ = new List<long>();
		private long[] minFactors_;

		public IReadOnlyList<long> Primes { get { return primes_; } }

		public Sieve(long n)
		{
			minFactors_ = new long[n + 1];
			Eratosthenes(n);
		}

		public bool IsPrime(long n)
		{
			return minFactors_[n] == n;
		}

		public IReadOnlyList<long> GetPrimeFactorList(long n)
		{
			var factors = new List<long>();
			while (n > 1) {
				factors.Add(minFactors_[n]);
				n /= minFactors_[n];
			}

			return factors;
		}

		public Dictionary<long, int> GetPrimeFactors(long n)
		{
			var factors = new Dictionary<long, int>();
			var list = GetPrimeFactorList(n);
			foreach (long value in list) {
				if (factors.ContainsKey(value)) {
					factors[value]++;
				} else {
					factors[value] = 1;
				}
			}

			return factors;
		}

		public Dictionary<long, int> GetPrimeFactorsOfLcm(IReadOnlyList<long> values)
		{
			var factors = new Dictionary<long, int>();
			foreach (long value in values) {
				var temp = GetPrimeFactors(value);
				foreach (long key in temp.Keys) {
					if (factors.ContainsKey(key)) {
						factors[key] = Math.Max(factors[key], temp[key]);
					} else {
						factors[key] = temp[key];
					}
				}
			}

			return factors;
		}

		private void Eratosthenes(long n)
		{
			minFactors_[0] = -1;
			minFactors_[1] = -1;

			for (long i = 2; i <= n; i++) {
				if (minFactors_[i] == 0) {
					primes_.Add(i);
					minFactors_[i] = i;
					for (long j = i * i; j <= n; j += i) {
						if (minFactors_[j] == 0) {
							minFactors_[j] = i;
						}
					}
				}
			}
		}
	}

	public static class Helper
	{
		public static void UpdateMin<T>(ref T target, T value) where T : IComparable<T>
			=> target = target.CompareTo(value) > 0 ? value : target;
		public static void UpdateMax<T>(ref T target, T value) where T : IComparable<T>
			=> target = target.CompareTo(value) < 0 ? value : target;

		public static T[] Array<T>(int n, Func<int, T> init)
			=> Enumerable.Range(0, n).Select(x => init(x)).ToArray();
		public static List<T> List<T>(int n, Func<int, T> init)
			=> Enumerable.Range(0, n).Select(x => init(x)).ToList();
		public static T[,] Array2<T>(int n, int m, T init)
		{
			var array = new T[n, m];
			for (int i = 0; i < n; i++) {
				for (int j = 0; j < m; j++) {
					array[i, j] = init;
				}
			}

			return array;
		}

		public static T[,,] Array3<T>(int n1, int n2, int n3, T init)
		{
			var array = new T[n1, n2, n3];
			for (int i1 = 0; i1 < n1; i1++) {
				for (int i2 = 0; i2 < n2; i2++) {
					for (int i3 = 0; i3 < n3; i3++) {
						array[i1, i2, i3] = init;
					}
				}
			}

			return array;
		}

		private static readonly int[] delta4_ = { 1, 0, -1, 0, 1 };
		public static void DoAt4(int i, int j, int imax, int jmax, Action<int, int> action)
		{
			for (int n = 0; n < 4; n++) {
				int ii = i + delta4_[n];
				int jj = j + delta4_[n + 1];
				if ((uint)ii < (uint)imax && (uint)jj < (uint)jmax) {
					action(ii, jj);
				}
			}
		}
	}

	public class Scanner2
	{
		private readonly char[] delimiter_ = new char[] { ' ' };
		private readonly string filePath_;
		private readonly Func<string> reader_;
		private string[] buf_;
		private int index_;

		public Scanner2(string file = "")
		{
			if (string.IsNullOrWhiteSpace(file)) {
				reader_ = Console.ReadLine;
			} else {
				filePath_ = file;
				var fs = new StreamReader(file);
				reader_ = fs.ReadLine;
			}
			buf_ = new string[0];
			index_ = 0;
		}

		public string Next()
		{
			if (index_ < buf_.Length) {
				return buf_[index_++];
			}

			string st = reader_();
			while (st == "") {
				st = reader_();
			}

			buf_ = st.Split(delimiter_, StringSplitOptions.RemoveEmptyEntries);
			if (buf_.Length == 0) {
				return Next();
			}

			index_ = 0;
			return buf_[index_++];
		}

		public int Int() => int.Parse(Next());
		public long Long() => long.Parse(Next());
		public double Double() => double.Parse(Next());

		public int[] ArrayInt(int N, int add = 0)
		{
			int[] Array = new int[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Int() + add;
			}
			return Array;
		}

		public long[] ArrayLong(int N, long add = 0)
		{
			long[] Array = new long[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Long() + add;
			}
			return Array;
		}

		public double[] ArrayDouble(int N, double add = 0)
		{
			double[] Array = new double[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Double() + add;
			}
			return Array;
		}

		public void Save(string text)
		{
			if (string.IsNullOrWhiteSpace(filePath_)) {
				return;
			}

			File.WriteAllText(filePath_ + "_output.txt", text);
		}
	}
}