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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.util.List;
import java.util.Map;
import java.util.NoSuchElementException;
import java.util.Random;
public class Main {
	static final long C =  1000000007;
	static final int CY = 1000000000;
	static final int INF = Integer.MAX_VALUE/2;
	StringBuilder sb;
	//セット
	class Set<F,S> {
		F f;
		S s;
		Set(F f, S s) {this.f = f;this.s = s;}
	}
	int[][] G;
	Map<Integer,List<Integer>> Genb = new HashMap<>();
	int V;
	int E;
	int Venb;
	int Eenb;
	long START_TIME;
	int GenbSize;//Genbグラフの1辺
	Random rand = new Random();
	public void calc() {

		sb = new StringBuilder();


		//入力処理
		IO sc = new IO();
		int n = sc.nextInt();
		int[] l = new int[n], r = new int[n];
		for (int i=0; i <n;i++) {
			l[i] = sc.nextInt();
			r[i] = sc.nextInt();

		}
		memo[1] = true;
		for (int i=4; i < memo.length; i+=2) {
			memo[i] = true;
			if (i*2-1 < memo.length) {
				memo[i *2 -1] = true;
			}
		}
		for (int i=3; i <memo.length; i+=2) {

			if(memo[i])continue;
			for (int t=i*2; t <memo.length; t+=i) {
				memo[t] = true;
			}
		}
		memo2[1] = true;
		for (int i=4; i < memo.length; i+=2) {
			memo2[i] = true;
			if (i*2-1 < memo.length) {
				memo2[i *2 -1] = true;
			}
		}
		for (int i=3; i <memo.length; i+=2) {

			if(memo[i])continue;
			for (int t=i*2; t <memo.length; t+=i) {
				memo2[t] = true;
				if (t*2-1 < memo.length) {
					memo2[t *2 -1] = true;
				}
			}
		}



		long[] ans = new long[n];
		int[] num = new int[100];
		for (int t=1; t <= 100000; t+=2) {

			if (!memo2[t]) {
				num[t/1000]++;
			}
		}

		for( int i=0; i < n; i++) {
			for (int t=l[i]; t <= r[i]; t+=2) {

				if (t %1000 == 1 && t + 1000 <= r[i])  {
					ans[i] += num[t/1000];
					t += 1000-2;
					continue;
				}

				if (!memo2[t]) {
					ans[i]++;
				}
			}
		}

		for (int i=0;i < n; i++) {
			System.out.println(ans[i]);
		}



	}
	boolean[] memo=new boolean[100010];
	boolean[] memo2=new boolean[100010];
	//素数判定
	boolean isPrime(int n) {

		return !memo2[n];



	}

	public static void main(String[] args) {
		Main main = new Main();
		main.calc();

	}
}
class IO extends PrintWriter {
	private final InputStream in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;

	public IO() { this(System.in);}
	public IO(InputStream source) { super(System.out); this.in = source;}
	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		}else{
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) {
				return false;
			}
		}
		return true;
	}
	private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
	private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
	private static boolean isNewLine(int c) { return c == '\n' || c == '\r';}
	public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
	public boolean hasNextLine() { while(hasNextByte() && isNewLine(buffer[ptr])) ptr++; return hasNextByte();}
	public String next() {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while(isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	public char[] nextCharArray(int len) {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		char[] s = new char[len];
		int i = 0;
		int b = readByte();
		while(isPrintableChar(b)) {
			if (i == len) {
				throw new InputMismatchException();
			}
			s[i++] = (char) b;
			b = readByte();
		}
		return s;
	}
	public String nextLine() {
		if (!hasNextLine()) {
			throw new NoSuchElementException();
		}
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while(!isNewLine(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	public long nextLong() {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while(true){
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			}else if(b == -1 || !isPrintableChar(b)){
				return minus ? -n : n;
			}else{
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}
	public int nextInt() {
		long nl = nextLong();
		if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) {
			throw new NumberFormatException();
		}
		return (int) nl;
	}
	public char nextChar() {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		return (char) readByte();
	}
	public double nextDouble() { return Double.parseDouble(next());}
	public int[] nextIntArray(int n) { int[] a = new int[n]; for(int i=0;i<n;i++) a[i] = nextInt(); return a;}
	public long[] nextLongArray(int n) { long[] a = new long[n]; for(int i=0;i<n;i++) a[i] = nextLong(); return a;}
	public double[] nextDoubleArray(int n) { double[] a = new double[n]; for(int i=0;i<n;i++) a[i] = nextDouble(); return a;}
	public void nextIntArrays(int[]... a) { for(int i=0;i<a[0].length;i++) for(int j=0;j<a.length;j++) a[j][i] = nextInt();}
	public int[][] nextIntMatrix(int n,int m) { int[][] a = new int[n][]; for(int i=0;i<n;i++) a[i] = nextIntArray(m); return a;}
	public char[][] nextCharMap(int n,int m) { char[][] a = new char[n][]; for(int i=0;i<n;i++) a[i] = nextCharArray(m); return a;}
	public void close() { super.close(); try {in.close();} catch (IOException e) {}}
}