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: Accepted)


import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.List;
import java.util.Scanner;
import java.util.Set;
import java.util.stream.Collectors;
import java.util.stream.IntStream;

public class Main {
    private static final int MAX = (int) 1e5 + 1;

    public static void main(final String[] args) {
        final Scanner scanner = new Scanner(System.in);
        final int q = scanner.nextInt();
        final int[] like2017 = new int[MAX];
        final Set<Integer> primeNumbers = sieveOfEratosthenes(MAX);

        for (int i = 1; i < MAX; i++) {
            like2017[i] = isLike2017(i, primeNumbers) ? like2017[i - 1] + 1 : like2017[i - 1];
        }

        for (int i = 0; i < q; i++) {
            final int begin = scanner.nextInt();
            final int end = scanner.nextInt();
            System.out.println(like2017[end] - like2017[begin - 1]);
        }
    }

    private static boolean isLike2017(final int number, final Set<Integer> primeNumbers) {
        return number % 2 == 1 && primeNumbers.contains(number) && primeNumbers.contains((number + 1) / 2);
    }

    private static Set<Integer> sieveOfEratosthenes(final int number) {
        List<Integer> numbers = IntStream.rangeClosed(2, number)
                .boxed()
                .collect(Collectors.toList());

        final int sqrt = (int) Math.sqrt(number);
        final Set<Integer> primeNumbers = new HashSet<>();
        int condition;

        do {
            final int prime = numbers.get(0);
            primeNumbers.add(prime);
            numbers = numbers.stream()
                    .filter(i -> i % prime != 0)
                    .collect(Collectors.toList());
            condition = prime;
        } while (condition < sqrt);

        primeNumbers.addAll(numbers);
        return primeNumbers;
    }
}