**PROBLEM LINK:**

**Author:** rahul_ojha_07

**Tester:** rahul_ojha_07

**DIFFICULTY:**

EASY

**PREREQUISITES:**

Prime Numbers, Sieve of Eratosthenes

**PROBLEM:**

Find the number of Prime number within a Range **N** That when added 6 to it also gives a Prime Number.

**EXPLANATION:**

The problem is to find the number of Prime number within a range **N** which gives a prime number when added 6 to it.

For solving the problem we can create an Array of prime numbers using Sieve of Eratosthenes.

```
for(int p=2;p*p ≤ n;p+=1)
{
if(prime[p]==true)
{
for(int i=p*p;i ≤ n;i+=p)
{
prime[i]=false;
}
}
}
```

Then for checking if a prime number gives a prime number on adding 6 . we need to initialize a counter variable **Count = 0** and iterating over the array using a loop and for each loop checking if a number of prime at certain index **i** then the index **i+6** should also be a prime number if this is the case we can increase the **Count** by one iterating over the array for **N** times we can count the number of Hex Prime.

The Implementation for the above statement is given below.

```
int c=0;
for(int p=2;p ≤ N;p+=1)
{
if(prime[p]==true and prime[p+6]==true)
c+=1;
}
```

To know more about this property of Prime number click here

**Author’s solution can be found here.**