Example: Optimized Prime Finder in Range in C++

// Optimized Prime Finder in Range
#include <iostream>
#include <cmath> // Required for sqrt() function

// Function to check if a single number is prime using optimized trial division
bool isPrimeOptimized(int n) {
    if (n <= 1) { // Numbers less than or equal to 1 are not prime
        return false;
    }
    if (n <= 3) { // 2 and 3 are prime
        return true;
    }
    if (n % 2 == 0 || n % 3 == 0) { // Eliminate multiples of 2 and 3 quickly
        return false;
    }
    // Check for divisors from 5 onwards, skipping multiples of 2 and 3
    // All primes greater than 3 can be expressed in the form 6k +/- 1
    for (int i = 5; i * i <= n; i = i + 6) {
        if (n % i == 0 || n % (i + 2) == 0) {
            return false;
        }
    }
    return true; // If no divisors found, it's prime
}

int main() {
    // Step 1: Define the range
    int lowerBound = 10;
    int upperBound = 30;

    std::cout << "Prime numbers in range [" << lowerBound << ", " << upperBound << "] (Optimized):" << std::endl;

    // Step 2: Iterate through each number in the range
    for (int i = lowerBound; i <= upperBound; ++i) {
        // Step 3: Check if the current number is prime using the optimized function
        if (isPrimeOptimized(i)) {
            std::cout << i << " "; // Print if it's prime
        }
    }
    std::cout << std::endl;

    return 0;
}