Problem Statement:

Given a number N, let CP(N) denote the number of primes between 1 and N (inclusive of N). We call N a prime counter if CP(N) is a prime (N need not be a prime).
For example, CP(3) = 2, CP(4) = 2, CP(5) = 2, CP(7) = 4.

Input Format:

First-line contains an integer T, a number of test cases. Next T lines each containing two positive integers L, R separated by space.

Output Format:

T lines containing the number of prime counters between L and R (both inclusive) in the ith test case (or NONE is no prime counter exists in that range).

L ≤ R ≤ 106

Example 1:

```Input: 1
1 10
Output: 4```

Example 2:

```Input: 2
2 20
21 30
Output: 8
NONE```

Code

```import java.util.*;
import java.io.*;

class Innoskrit {

public static void primeCounters(int ranges[][], int size) {

boolean primeSieve[] = new boolean[size + 1];
Arrays.fill(primeSieve, true);
int cp[] = new int[size + 1];
int primeCounters[] = new int[size + 1];

primeSieve[0] = false;
primeSieve[1] = false;

for(int number = 2; number <= size; number++) {

if(primeSieve[number]) {
cp[number] = cp[number - 1] + 1;
} else {
cp[number] = cp[number - 1];
}

if(primeSieve[cp[number]]) {
primeCounters[number] = primeCounters[number - 1] + 1;
} else {
primeCounters[number] = primeCounters[number - 1];
}

if(primeSieve[number]) {
for(int multiple = number*number; multiple <= size; multiple += number) {
primeSieve[multiple] = false;
}
}
}

for(int[] range : ranges) {
int ans = primeCounters[range[1]] - primeCounters[range[0] - 1];
if(ans == 0)
System.out.println("NONE");
else
System.out.println(ans);
}
}

public static void main(String[] args) throws IOException {

int ranges[][] = new int[testcases][2];
int maxNumber = 0;

for(int t = 0; t < testcases; t++) {
ranges[t][0] = Integer.parseInt(range[0]);
ranges[t][1] = Integer.parseInt(range[1]);
maxNumber = Math.max(maxNumber, ranges[t][1]);
}

primeCounters(ranges, maxNumber);
}
}```
```#include <bits/stdc++.h>
using namespace std;

void primeCounters(vector<pair<int, int>> &ranges, int size) {

vector<bool> primeSieve(size + 1, true);
vector<int> cp(size + 1, 0);
vector<int> primeCounter(size + 1, 0);

primeSieve[0] = false;
primeSieve[1] = false;

for(int number = 2; number <= size; number++) {

if(primeSieve[number]) {
cp[number] = cp[number - 1] + 1;
} else {
cp[number] = cp[number - 1];
}

if(primeSieve[cp[number]]) {
primeCounter[number] = primeCounter[number - 1] + 1;
} else {
primeCounter[number] = primeCounter[number - 1];
}

if(primeSieve[number]) {
for(int multiple = number * number; multiple <= size; multiple += number) {
primeSieve[multiple] = false;
}
}
}
for(auto range : ranges) {
int ans = primeCounter[range.second] - primeCounter[range.first - 1];
if(ans == 0) {
cout << "NONE" << endl;
} else {
cout << ans << endl;
}
}
}

int main() {

int testcases;
cin >> testcases;
vector<pair<int, int>> ranges(testcases);
int maxNumber = 0;

for(int t = 0; t < testcases; t++) {
int l, r;
cin >> l >> r;
ranges[t] = {l, r};
maxNumber = max(maxNumber, r);
}

primeCounters(ranges, maxNumber);

return 0;
}```
```def prime_counters(ranges, size):

prime_sieve = [True] * (size + 1)
cp = [0] * (size + 1)
prime_counters = [0] * (size + 1)

prime_sieve[0] = False
prime_sieve[1] = False

for number in range(2, size + 1):
if prime_sieve[number] is True:
cp[number] = cp[number - 1] + 1
else:
cp[number] = cp[number - 1]

if prime_sieve[cp[number]] is True:
prime_counters[number] = prime_counters[number - 1] + 1
else:
prime_counters[number] = prime_counters[number - 1]

if prime_sieve[number] is True:
for multiple in range(number*number, size + 1, number):
prime_sieve[multiple] = False

for l, r in ranges:
ans = prime_counters[r] - prime_counters[l - 1]
if ans == 0:
print("NONE")
else:
print(ans)

if __name__ == '__main__':

testcases = int(input())
ranges = []
max_number = 0

for t in range(testcases):
l, r = tuple(map(int, input().split()))
ranges.append((l, r))
max_number = max(max_number, r)

prime_counters(ranges, max_number)
```