Check Whether an Integer is Prime or Composite

Given a positive integer N, determine whether it is a Prime number, Composite number, or Neither (<= 1) using an optimized trial division loop running up to sqrt(N).

Step 1: Start.
Step 2: Read integer N.
Step 3: If N <= 1:
         Print 'Neither Prime nor Composite' and Stop.
Step 4: If N == 2 or N == 3:
         Print 'Prime Number' and Stop.
Step 5: If N % 2 == 0:
         Print 'Composite Number' and Stop.
Step 6: Initialize i = 3.
Step 7: While (i * i <= N):
         If (N % i == 0):
             Print 'Composite Number' and Stop.
         i = i + 2.
Step 8: Print 'Prime Number'.
Step 9: Stop.

         +-----------------+
         |     [ START ]   |
         +-----------------+
                  |
                  v
         +-----------------+
         |     Read N      |
         +-----------------+
                  |
                  v
               /     \
             / N <= 1?\ ---YES--> [Print Neither] --> [STOP]
             \       /
                  | NO
                  v
               /     \
             / N==2,3?\ ---YES--> [Print Prime]   --> [STOP]
             \       /
                  | NO
                  v
               /     \
             / N%2==0?\ ---YES--> [Print Composite]--> [STOP]
             \       /
                  | NO
                  v
         +-----------------+
         |    Set i = 3    |
         +-----------------+
                  |
                  v
               /     \
             /i*i <= N?\ ---NO---> [Print Prime]   --> [STOP]
             \       /
                  | YES
                  v
               /     \
             / N%i==0?\ ---YES--> [Print Composite]--> [STOP]
             \       /
                  | NO
                  v
         +-----------------+
         |    i = i + 2    | ----> (Loop to i*i <= N)
         +-----------------+

Edit the code directly with the Edit Code button, provide custom inputs, and press Run Code to compile and execute in the live terminal console below!

#include <iostream>
using namespace std;

int main() {
    long long n;
    cout << "Enter a positive integer: ";
    if (!(cin >> n)) {
        cout << "Invalid input! Please enter a valid integer.\n";
        return 1;
    }

    if (n <= 1) {
        cout << n << " is NEITHER prime nor composite (by definition).\n";
        return 0;
    }
    if (n == 2 || n == 3) {
        cout << n << " is a PRIME number.\n";
        return 0;
    }
    if (n % 2 == 0) {
        cout << n << " is a COMPOSITE number (divisible by 2).\n";
        return 0;
    }

    bool isPrime = true;
    for (long long i = 3; i * i <= n; i += 2) {
        if (n % i == 0) {
            isPrime = false;
            cout << n << " is a COMPOSITE number (divisible by " << i << ").\n";
            break;
        }
    }

    if (isPrime) {
        cout << n << " is a PRIME number.\n";
    }
    return 0;
}

Input:
997

Output:
997 is a PRIME number.