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Balanced Prime in C++
Balanced prime number is a prime number that has the same difference for its previous and next prime numbers. i.e. it is the mean of the nearest next prime and previous prime.
For a prime number to be a balanced prime, it should follow the following formula −
Pn = (P(n-1) + P(n+1)) / 2
Where n is the index of the prime number pn in the ordered set of a prime number.
The ordered set of prime numbers: 2, 3, 5, 7, 11, 13,….
First, balanced primes are 5, 53, 157, 173 , …
In this problem, we are given a number n and we have to find an nth balanced prime number.
Let’s take an example,
Input : n = 3 Output : 157
For this will generate prime numbers and store it in an array. We will find whether the prime number is a balanced prime or not. If it increases the count and if the count is equal to n, print it.
Example
#include<bits/stdc++.h>
#define MAX 501
using namespace std;
int balancedprimenumber(int n){
bool prime[MAX+1];
memset(prime, true, sizeof(prime));
for (int p = 2; p*p <= MAX; p++){
if (prime[p] == true)
{
for (int i = p*2; i <= MAX; i += p)
prime[i] = false;
}
}
vector<int> v;
for (int p = 3; p <= MAX; p += 2)
if (prime[p])
v.push_back(p);
int count = 0;
for (int i = 1; i < v.size(); i++){
if (v[i] == (v[i+1] + v[i - 1])/2)
count++;
if (count == n)
return v[i];
}
}
int main(){
int n = 3;
cout<<balancedprimenumber(n)<<endl;
return 0;
}Output
157
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