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Prime Number in C++

To determine whether a given number is prime in C++, you can use a simple algorithm that checks if the number is divisible by any integers from 2 to the square root of the number. If it’s not divisible by any of these integers, it’s a prime number. Here’s a C++ program to check for prime numbers:

C++
#include <iostream>
#include <cmath>

bool isPrime(int number) {
    if (number <= 1) {
        return false; // 0 and 1 are not prime
    }
    if (number <= 3) {
        return true; // 2 and 3 are prime
    }
    if (number % 2 == 0 || number % 3 == 0) {
        return false; // Numbers divisible by 2 or 3 are not prime
    }

    // Check for prime by testing divisors from 5 to the square root of the number
    for (int i = 5; i * i <= number; i += 6) {
        if (number % i == 0 || number % (i + 2) == 0) {
            return false; // Number is divisible by i or i+2, so it's not prime
        }
    }

    return true; // If no divisors were found, the number is prime
}

int main() {
    int n;
    std::cout << "Enter a number: ";
    std::cin >> n;

    if (isPrime(n)) {
        std::cout << n << " is a prime number." << std::endl;
    } else {
        std::cout << n << " is not a prime number." << std::endl;
    }

    return 0;
}

In this program:

  1. We first handle special cases: 0 and 1 are not prime, and 2 and 3 are prime.
  2. We use a loop to check for divisibility starting from 5 up to the square root of the number. We increment i by 6 in each iteration because we have already checked divisibility by 2 and 3, so we only need to consider numbers of the form 6k ± 1.
  3. Within the loop, we check if the number is divisible by i or i + 2. If it is, we return false because it’s not prime.
  4. If none of the divisors were found, the number is considered prime, and we return true.

This program allows you to input a number, and it will tell you whether that number is prime or not.

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