Java

    public static List<Integer> PRIME_NUMBERS = new ArrayList<>();

public static String sillyGame(int n) {
int numberOfPrimes = PRIME_NUMBERS.size();
    Integer largestPrimeNumber = numberOfPrimes > 0 ? PRIME_NUMBERS.get(numberOfPrimes -1) : 0;
    if (numberOfPrimes == 0) {
        for (int i = 2; i <= n; i++) {
            if (isPrime(i)) PRIME_NUMBERS.add(i);
        }
    } else if (n >= largestPrimeNumber) {
        for (int i = largestPrimeNumber + 1; i <=n; i++) {
            if (isPrime(i)) PRIME_NUMBERS.add(i);
        }
    } else {
        PRIME_NUMBERS.removeIf(p -> p > n);
    }
    return PRIME_NUMBERS.size() % 2 == 0 ? "Bob" : "Alice";    }

static  boolean isPrime(int num)
{
    if (num <= 1) return false;
    for (int i = 2; i <= Math.sqrt(num); i++) {
        if (num % i == 0) return false;
    }
    return true;
}