Given **two integers L and R**, the task to find the number of Double Prime numbers in the range.

A number N is called

double primewhen the count of prime numbers in the range 1 to N(excluding 1 and including N)is also prime.

**Examples:**

Input:L = 3, R = 10

Output:4

Explanation:

For 3, we have the range 1, 2, 3, and count of prime number is 2 (which is also a prime no.)

For 4, we have the range 1, 2, 3, 4, and count of a prime number is 2 (which is also a prime no.)

For 5, we have the range 1, 2, 3, 4, 5, and count of a prime number is 3 (which is also a prime no.)

For 6, we have the range 1, 2, 3, 4, 5, 6, and count of prime numbers is 3 (which is also a prime no.)

For 7, we have the range 1, 2, 3, 4, 5, 6, 7, and count of prime numbers is 4 which is nonprime.

Similarly for other numbers till R = 10, the count of prime numbers is nonprime. Hence the count of double prime numbers is 4.

Input:L = 4, R = 12

Output:5

Explanation:

For the given range there are total 5 double prime numbers.

**Approach:**

To solve the problem mentioned above we will use the concept of Sieve to generate prime numbers.

- Generate all prime numbers for 0 to 10
^{6}and store in an array. - Initialize a variable
*count*to keep a track of prime numbers from 1 to some ith position. - Then for every prime number we will increment the count and also set dp[count] = 1 (where dp is the array which stores a double prime number) indicating the number of numbers from 1 to some ith position that are prime.
- Lastly, find the cumulative sum of dp array so the answer will be
**dp[R] – dp[L – 1]**.

Below is the implementation of the above approach:

## C++

`// C++ program to find the count ` `// of Double Prime numbers ` `// in the range L to R ` ` ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Array to make Sieve ` `// where arr[i]=0 indicates ` `// non prime and arr[i] = 1 ` `// indicates prime ` `int` `arr[1000001]; ` ` ` `// Array to find double prime ` `int` `dp[1000001]; ` ` ` `// Function to find the number ` `// double prime numbers in range ` `void` `count() ` `{ ` ` ` `int` `maxN = 1000000, i, j; ` ` ` ` ` `// Assume all numbers as prime ` ` ` `for` `(i = 0; i < maxN; i++) ` ` ` `arr[i] = 1; ` ` ` ` ` `arr[0] = 0; ` ` ` `arr[1] = 0; ` ` ` ` ` `for` `(i = 2; i * i <= maxN; i++) { ` ` ` ` ` `// Check if the number is prime ` ` ` `if` `(arr[i] == 1) { ` ` ` ` ` `// check for multiples of i ` ` ` `for` `(j = 2 * i; j <= maxN; j += i) { ` ` ` ` ` `// Make all multiples of ` ` ` `// ith prime as non-prime ` ` ` `arr[j] = 0; ` ` ` `} ` ` ` `} ` ` ` `} ` ` ` ` ` `int` `cnt = 0; ` ` ` ` ` `for` `(i = 0; i <= maxN; i++) { ` ` ` `// Check if number at ith position ` ` ` `// is prime then increment count ` ` ` `if` `(arr[i] == 1) ` ` ` `cnt++; ` ` ` ` ` `if` `(arr[cnt] == 1) ` ` ` ` ` `// Indicates count of numbers ` ` ` `// from 1 to i that are ` ` ` `// also prime and ` ` ` `// hence double prime ` ` ` `dp[i] = 1; ` ` ` ` ` `else` ` ` `// If number is not a double prime ` ` ` `dp[i] = 0; ` ` ` `} ` ` ` `for` `(i = 1; i <= maxN; i++) ` ` ` `// finding cumulative sum ` ` ` `dp[i] += dp[i - 1]; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `int` `L = 4, R = 12; ` ` ` `count(); ` ` ` `cout << dp[R] - dp[L - 1]; ` ` ` ` ` `return` `0; ` `} ` |

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## Java

`// Java program to find the count ` `// of Double Prime numbers ` `// in the range L to R ` `import` `java.util.*; ` `import` `java.lang.*; ` `class` `GFG{ ` ` ` `// Array to make Sieve ` `// where arr[i]=0 indicates ` `// non prime and arr[i] = 1 ` `// indicates prime ` `static` `int` `[] arr = ` `new` `int` `[` `1000001` `]; ` ` ` `// Array to find double prime ` `static` `int` `[] dp = ` `new` `int` `[` `1000001` `]; ` ` ` `// Function to find the number ` `// double prime numbers in range ` `static` `void` `count() ` `{ ` ` ` `int` `maxN = ` `1000000` `, i, j; ` ` ` ` ` `// Assume all numbers as prime ` ` ` `for` `(i = ` `0` `; i < maxN; i++) ` ` ` `arr[i] = ` `1` `; ` ` ` ` ` `arr[` `0` `] = ` `0` `; ` ` ` `arr[` `1` `] = ` `0` `; ` ` ` ` ` `for` `(i = ` `2` `; i * i <= maxN; i++) ` ` ` `{ ` ` ` ` ` `// Check if the number is prime ` ` ` `if` `(arr[i] == ` `1` `) ` ` ` `{ ` ` ` ` ` `// check for multiples of i ` ` ` `for` `(j = ` `2` `* i; j <= maxN; j += i) ` ` ` `{ ` ` ` ` ` `// Make all multiples of ` ` ` `// ith prime as non-prime ` ` ` `arr[j] = ` `0` `; ` ` ` `} ` ` ` `} ` ` ` `} ` ` ` ` ` `int` `cnt = ` `0` `; ` ` ` ` ` `for` `(i = ` `0` `; i <= maxN; i++) ` ` ` `{ ` ` ` `// Check if number at ith position ` ` ` `// is prime then increment count ` ` ` `if` `(arr[i] == ` `1` `) ` ` ` `cnt++; ` ` ` ` ` `if` `(arr[cnt] == ` `1` `) ` ` ` ` ` `// Indicates count of numbers ` ` ` `// from 1 to i that are ` ` ` `// also prime and ` ` ` `// hence double prime ` ` ` `dp[i] = ` `1` `; ` ` ` ` ` `else` ` ` `// If number is not a double prime ` ` ` `dp[i] = ` `0` `; ` ` ` `} ` ` ` ` ` `for` `(i = ` `1` `; i <= maxN; i++) ` ` ` ` ` `// finding cumulative sum ` ` ` `dp[i] += dp[i - ` `1` `]; ` `} ` ` ` `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` ` ` `int` `L = ` `4` `, R = ` `12` `; ` ` ` `count(); ` ` ` `System.out.println(dp[R] - dp[L - ` `1` `]); ` `} ` `} ` ` ` `// This code is contributed by offbeat ` |

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## C#

`// C# program to find the count ` `// of Double Prime numbers ` `// in the range L to R ` `using` `System; ` `class` `GFG{ ` ` ` `// Array to make Sieve ` `// where arr[i]=0 indicates ` `// non prime and arr[i] = 1 ` `// indicates prime ` `static` `int` `[] arr = ` `new` `int` `[1000001]; ` ` ` `// Array to find double prime ` `static` `int` `[] dp = ` `new` `int` `[1000001]; ` ` ` `// Function to find the number ` `// double prime numbers in range ` `static` `void` `count() ` `{ ` ` ` `int` `maxN = 1000000, i, j; ` ` ` ` ` `// Assume all numbers as prime ` ` ` `for` `(i = 0; i < maxN; i++) ` ` ` `arr[i] = 1; ` ` ` ` ` `arr[0] = 0; ` ` ` `arr[1] = 0; ` ` ` ` ` `for` `(i = 2; i * i <= maxN; i++) ` ` ` `{ ` ` ` ` ` `// Check if the number is prime ` ` ` `if` `(arr[i] == 1) ` ` ` `{ ` ` ` ` ` `// check for multiples of i ` ` ` `for` `(j = 2 * i; j <= maxN; j += i) ` ` ` `{ ` ` ` ` ` `// Make all multiples of ` ` ` `// ith prime as non-prime ` ` ` `arr[j] = 0; ` ` ` `} ` ` ` `} ` ` ` `} ` ` ` ` ` `int` `cnt = 0; ` ` ` ` ` `for` `(i = 0; i <= maxN; i++) ` ` ` `{ ` ` ` `// Check if number at ith position ` ` ` `// is prime then increment count ` ` ` `if` `(arr[i] == 1) ` ` ` `cnt++; ` ` ` ` ` `if` `(arr[cnt] == 1) ` ` ` ` ` `// Indicates count of numbers ` ` ` `// from 1 to i that are ` ` ` `// also prime and ` ` ` `// hence double prime ` ` ` `dp[i] = 1; ` ` ` ` ` `else` ` ` `// If number is not a double prime ` ` ` `dp[i] = 0; ` ` ` `} ` ` ` ` ` `for` `(i = 1; i <= maxN; i++) ` ` ` ` ` `// finding cumulative sum ` ` ` `dp[i] += dp[i - 1]; ` `} ` ` ` `// Driver code ` `public` `static` `void` `Main() ` `{ ` ` ` `int` `L = 4, R = 12; ` ` ` `count(); ` ` ` `Console.Write(dp[R] - dp[L - 1]); ` `} ` `} ` ` ` `// This code is contributed by Code_Mech ` |

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**Output:**

5

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