🏰 Prime Castle Sieve Defense

📚 Sieve of Eratosthenes

Ancient algorithm to find all primes up to N:

1. Start with all numbers 2 to N (unmarked = potentially prime)
2. Find the smallest unmarked number (it's prime!)
3. Mark all its multiples as composite (2p, 3p, 4p, ...)
4. Repeat until you've processed all numbers up to √N
5. All remaining unmarked numbers are prime! 🎉

Time Complexity: O(N log log N) - very efficient!