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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"bytes"
	"fmt"
	"io"
	"os"
	"strconv"
	"sort"
	"math"
)

// -----------------------------------------------------------------------------

// IO helper functions

// Returns next token from input.  It must be initialized by SetInput()
// before the first call.
var nextToken func() ([]byte, error)
var nextLine func() ([]byte, error)

// Holds a buffer for output.  It must be initialized by SetOutput().
// All IO fucntions (read*() and [e]print*()) should write to OutputWriter
// instead of this.
var OutputBuffer *bufio.Writer

// Holds an io.Writer.  It must be initialized by SetOutput()
var OutputWriter io.Writer

// Set IO functions for interactive input/output.
func SetInteractive(w io.Writer, r io.Reader) {
	SetUnbefferedInput(r)
	OutputBuffer = nil
	OutputWriter = w
}

// Setup OutputBuffer and OutputWriter.
func SetOutput(w io.Writer) {
	OutputBuffer = bufio.NewWriter(w)
	OutputWriter = OutputBuffer
}

// Flushes OutputBuffer
func Flush() {
	if OutputBuffer != nil {
		OutputBuffer.Flush()
	}
}

// Returns true if c is a white space
func IsSpace(c byte) bool {
	switch c {
	case '\t', '\n', '\v', '\f', '\r', ' ':
		return true
	}
	return false
}

func IsNewLine(c byte) bool {
	switch c {
	case '\n', '\r':
		return true
	}
	return false
}

// Setup nextToken with input buffer.
func SetInput(r io.Reader) {
	buf := new(bytes.Buffer)
	var b []byte

	var i int
	rest := func() ([]byte, error) {
		for i < len(b) && IsSpace(b[i]) {
			i++
		}
		if i == len(b) {
			return nil, io.ErrUnexpectedEOF
		}
		j := i
		for i < len(b) && !IsSpace(b[i]) {
			i++
		}
		return b[j:i], nil
	}
	initial := func() ([]byte, error) {
		io.Copy(buf, r)
		b = buf.Bytes()
		nextToken = rest
		return rest()
	}
	nextToken = initial

	restLn := func() ([]byte, error) {
		for i < len(b) && IsNewLine(b[i]) {
			i++
		}
		if i == len(b) {
			return nil, io.ErrUnexpectedEOF
		}
		j := i
		for i < len(b) && !IsNewLine(b[i]) {
			i++
		}
		return b[j:i], nil
	}

	initialLn := func() ([]byte, error) {
		io.Copy(buf, r)
		b = buf.Bytes()
		nextLine = restLn
		return restLn()
	}
	nextLine = initialLn
}

// Setup nextToken without input buffer.
func SetUnbefferedInput(r io.Reader) {
	buf := bufio.NewReader(r)
	var b []byte

	var i int
	nextToken = func() ([]byte, error) {
		var err error
		if i == len(b) {
			b, err = buf.ReadBytes('\n')
			if err != nil {
				return nil, err
			}
			i = 0
			j := len(b) - 1
			for 0 <= j && IsSpace(b[j]) {
				j--
			}
			b = b[0 : j+1]
		}
		for i < len(b) && IsSpace(b[i]) {
			i++
		}
		j := i
		for i < len(b) && !IsSpace(b[i]) {
			i++
		}
		if i == j {
			return nil, io.ErrUnexpectedEOF
		}
		return b[j:i], nil
	}
}

// -----------------------------------------------------------------------------

// Reads next token and return it as string
func reads() string {
	b, err := nextToken()
	if err != nil {
		panic(err)
	}
	return string(b)
}

// Read next line as string
func readsln() string {
	b, err := nextLine()
	if err != nil {
		panic(err)
	}

	return string(b)
}

// Reads next token and return it as int
func readi() int {
	i, err := strconv.ParseInt(reads(), 10, 64)
	if err != nil {
		panic(err.Error())
	}

	return int(i)
}

// Reads next token and return it as float64
func readf() float64 {
	f, err := strconv.ParseFloat(reads(), 64)
	if err != nil {
		panic(err.Error())
	}
	return f
}

// ReadIntSlice returns an integer slice that has n integers.
func readislice(n int) []int {
	b := make([]int, n)
	for i := 0; i < n; i++ {
		b[i] = readi()
	}
	return b
}

// set up IO functions
func init() {
	// for non-interactive
	SetInput(os.Stdin)
	SetOutput(os.Stdout)

	// Enable below when interactive.  Its ok to leave above intact.
	// SetInteractive(os.Stdout, os.Stdin)
}

// -----------------------------------------------------------------------------

const (
	MOD = 1000000007
	INF = math.MaxInt64
)

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

func max(a, b int) int {
	if a < b {
		return b
	}
	return a
}

func abs(a int) int {
	if a < 0 {
		return -a
	}
	return a
}

func pow(p, q int) int {
    return int(math.Pow(float64(p), float64(q)))
}

// egcd(a, b) returns d, x, y:
//   d is gcd(a,b)
//   x, y are  integers that satisfy ax + by = d
func egcd(a, b int) (int, int, int) {
	if b == 0 {
		return a, 1, 0
	}
	d, x, y := egcd(b, a%b)
	return d, y, x - a/b*y
}

func gcd(a, b int) int {
	d, _, _ := egcd(a, b)
	return d
}

func lcm(a,b int) int{
  return a * b / gcd(a, b)
}

func isInteger(x float64) bool {
    return math.Floor(x) == x
}

// lower_bound
func bisectLeft(a []int, x int) int {
    return sort.SearchInts(a, x)
}

// upper_bound
func bisectRight(a []int, x int) int {
    return sort.Search(len(a), func(i int) bool { return a[i] > x })
}

func main() {
	defer Flush()

	Q := readi()
	L := make([]int, Q)
	R := make([]int, Q)

	for i := range L {
		L[i] = readi()
		R[i] = readi()
	}

	ns := make([]int, 100001)
	S := make([]int, 100002)
	primes := sieveOfEratosthenes(100001)

	for _, n := range primes {
		ns[n] = 1
	}

	n_like_2017 := make([]int, 100001)

	for i, v := range ns {
		if v != 1 {
			continue
		}


		if ns[((i + 1) / 2)] == 1 {
			n_like_2017[i]++
		}
	}

	S[0] = 0

	for i := range n_like_2017 {
		if i == 0 {
			continue
		}

		S[i] = S[i-1] + n_like_2017[i]
	}

	for i := range L {
		fmt.Println(S[R[i]] - S[L[i] - 1])
	}
}

func sieveOfEratosthenes(n int) []int {
	// Create a boolean array "prime[0..n]" and initialize
	// all entries it as true. A value in prime[i] will
	// finally be false if i is Not a prime, else true.
	integers := make([]bool, n+1)
	for i := 2; i < n+1; i++ {
			integers[i] = true
	}

	for p := 2; p*p <= n; p++ {
			// If integers[p] is not changed, then it is a prime
			if integers[p] == true {
					// Update all multiples of p
					for i := p * 2; i <= n; i += p {
							integers[i] = false
					}
			}
	}

	// return all prime numbers <= n
	var primes []int
	for p := 2; p <= n; p++ {
			if integers[p] == true {
					primes = append(primes, p)
			}
	}

	return primes
}