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-mcs 6.8.0.105) (judge verdict: Accepted)

using System;
using System.Collections;
using System.IO;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
using System.Collections.Generic;
using System.Threading.Tasks;

class Program
{
	//Main
	static void Main(string[] args)
	{
		//出力準備（AutoFlushを切る）
		var sw = new StreamWriter(Console.OpenStandardOutput()){AutoFlush = false};
		Console.SetOut(sw);
		//解答
		Solve();
		//出力終了
		Console.Out.Flush();
	}

	//与えられた整数n以下の素数をリストで返す関数
	//所謂「エラトステネスの篩」を使う。
	//タイプはintとする
	static List<int> SieveOfEratosthenes(int n)
	{
		//素数を格納するリスト
		List<int> primeNumbers = new List<int>();

		//検索用の配列を初期化
		int[] searchArr = new int[n+1];
		for(int i=0; i<n+1; i++){
			searchArr[i] = i;
		}

		//入力値の平方根
		int root = (int)Math.Sqrt(n);

		//現在の最小の素数
		int p = 2;

		//平方根を超えるまでループ
		while(p <= root){
			//素数ではない場合、次へ
			if(searchArr[p] == 0){
				p ++;
				continue;
			}
			//素数の場合
			else{
				//素数リストに加える
				primeNumbers.Add(p);

				//当該素数pで割り切れる数を全て排除
				//p^2から始めれば良い
				for(int i=p*p; i<n+1; i++){
					if(i % p == 0){
						searchArr[i] = 0;
					}
				}

				//pを次へ
				p++;
			}
		}

		//平方根を超えた以降も加える
		for(int i=root+1; i<n+1; i++){
			if(searchArr[i] != 0){
				primeNumbers.Add(i);
			}
		}

		//出力
		return primeNumbers;
	}

	//2017に似た数の合計数（累積和）
	static int[] numArr;

	//クエリに応答
	static void Answer(){
		string[] S = Console.ReadLine().Split(' ');
		int L = int.Parse(S[0]);
		int R = int.Parse(S[1]);

		//累積和から、個数を計算
		int ans = numArr[R-1];
		if(L > 1){
			ans -= numArr[L-2];
		}

		Console.WriteLine(ans);
	}

	static void Solve(){
		//読み込む
		int Q = int.Parse(Console.ReadLine());

		//素数のリストを取得
		int max = 100000;
		List<int> primeLs = SieveOfEratosthenes(max);

		//累積和の配列を埋める
		numArr = new int[max];
		for(int i=1; i<max; i++){
			numArr[i] += numArr[i-1];

			//i+1が2017に似た数かどうか調べる
			int num = i+1;
			int idx = primeLs.BinarySearch(num);
			//そもそも素数でない場合、次へ
			if(idx < 0 || max <= idx){
				continue;
			}
			else if(primeLs[idx] != num){
				continue;
			}
			else{
				//(N+1)/2が素数でない場合は飛ばす
				int num2 = (num+1)/2;
				int idx2 = primeLs.BinarySearch(num2);
				if(idx2 < 0 || max <= idx2){
					continue;
				}
				else if(primeLs[idx2] != num2){
					continue;
				}
				else{
					numArr[i] ++;
				}
			}
		}

		/*debug
		for(int i=0; i<max; i++){
			Console.Write("arr[{0}]={1}, ", i, numArr[i]);
		}
		*/

		//クエリに応答
		for(int i=0; i<Q; i++){
			Answer();
		}
	}
}