Example: Sieve of Eratosthenes Prime Finder in C++

// Sieve of Eratosthenes Prime Finder
#include <iostream>
#include <vector> // Required for std::vector

// Function to implement the Sieve of Eratosthenes
void sieveOfEratosthenes(int upperBound, std::vector<bool>& isPrime) {
    // Step 1: Initialize all entries as true. A value in isPrime[i] will be false if i is not prime, else true.
    isPrime.assign(upperBound + 1, true); // Resize and fill with true
    isPrime[0] = false; // 0 is not prime
    isPrime[1] = false; // 1 is not prime

    // Step 2: Start from the first prime number, 2
    for (int p = 2; p * p <= upperBound; ++p) {
        // If isPrime[p] is still true, then it is a prime
        if (isPrime[p] == true) {
            // Mark all multiples of p as not prime
            // Start from p*p because smaller multiples (p*2, p*3, etc.) would have already been marked
            // by smaller prime factors (2, 3, etc.)
            for (int i = p * p; i <= upperBound; i += p)
                isPrime[i] = false;
        }
    }
}

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

    // Step 2: Declare a boolean vector to store primality information
    // Its size will be upperBound + 1 to accommodate numbers from 0 to upperBound
    std::vector<bool> isPrime;

    // Step 3: Run the Sieve to populate the isPrime vector up to upperBound
    sieveOfEratosthenes(upperBound, isPrime);

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

    // Step 4: Iterate through the specified range and print primes based on the Sieve result
    // Ensure lowerBound is at least 0. If it's less, adjust to 0 for vector access.
    int start = (lowerBound < 0) ? 0 : lowerBound;
    if (start > upperBound) {
        std::cout << "Invalid range." << std::endl;
        return 0;
    }

    for (int i = start; i <= upperBound; ++i) {
        if (isPrime[i]) {
            std::cout << i << " ";
        }
    }
    std::cout << std::endl;

    return 0;
}