First time using std::vector<bool>. Decided to make a Sieve of Eratosthenes for practice. Takes a number for input and finds all the primes up to that number. Sieve[x] will return true if x is prime, false if not.

Sieve.cpp

#include <iostream> // Needed for std::cin/cout
#include <vector> // Needed for std::vector
#include <cmath> // Needed for sqrt and ceil

int main()
{
	/* Will be the sieve */
	std::vector<bool> Sieve;
	unsigned int x, y, limit;

	std::cout << "Enter the number to stop at: ";
	std::cin >> x;

	/* Resize the sieve to the size we input, we use x+1
		because vectors start counting at 0, and since
		we don't use 0 the actual number we need is 1
		higher than the vector. */
	Sieve.resize(x+1, true);

	/* We only have to check numbers under the square root of the number
		we're going to, any number higher than that, that isn't a
		multiple of a previous number will be prime. */
	limit = ceil(sqrt(x));

	/* Loop for every number up to limit */
	for (x = 2; x < limit; ++x)
		/* If this is true then we found a prime number */
		if (Sieve[x] == true)
			/* Loop the multiples of the prime found up to
				 Sieve.size() and set to false */
			for (y = x*2; y < Sieve.size(); y += x)
				Sieve[y] = false;

	/* Print the primes found. */
	for (x = 1; x < Sieve.size(); ++x)
		if (Sieve[x] == true)
			std::cout << "Prime: " << x << std::endl;


	return 0;
}