# C++ program to find largest list of prime numbers

Here, we are going to learn **how to find the largest list of prime numbers**?

Submitted by Debasis Jana, on January 28, 2019

**Problem statement:**

You are given a number **N**, you have to **find the largest list of prime numbers** that will give **N** after summation of the list.

**Example:**

Sample Input: 7 2 Sample Output: 2 2 3 2

**Explanation:**

7 can be expressed as summation of 2+2+3 2 can be expressed as summation of 2

**Basic Idea:**

A number can be expressed as summation of longest list of prime numbers only when it is expressed only with 2 and 3.

**Algorithm:**

prime_List(N)1. if(N%2)==0 2. Express it as summation of (N/2) number of 2 3. Else if(N%2)!=0 //So that N can be even, for example N=19, so now N=19-3=16 4. Set N=N-3 5. Print (N/2) numbers of 2 6. Print 3 7. END of Program.

**C++ program**

#include<bits/stdc++.h> using namespace std; int list_prime(int n) { int i; if(n<2) { cout<<"Summation not possible\n"; } //if n can be divided by 2, then we can express //it as summation of 2 only else if(n%2==0) { for(i=1;i<=n/2;i++) { cout<<2<<" "; } } else { //making the number even n=n-3; //n can be divided by 2 now for(i=1;i<=n/2;i++) cout<<2<<" "; //add 3, and the summation will be now n cout<<3<<" "; } } int main() { int i,n; cin>>n; list_prime(n); return 0; }

**Output**

7 2 2 3

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