Java

public static String sillyGame(int n) {
// Write your code here
     if(n==1 || n==3 || n==4 || n==7 || n==8 || n==9 || n==10 ){
         return "Bob";
     }
     if(n==2 || n==5 || n==6 ){
        return "Alice"; 
     }
     List<Integer> list=new ArrayList<>();
     List<Integer> li=new ArrayList<>();
     li.add(2);
     li.add(3);
     li.add(5);
     li.add(7);

     for(int i=11;i<=n;i++){
    if(i%2==0 || i%3==0 || i%4==0 || i%5==0 || i%6==0 || i%7==0 || i%8==0 || i%9==0 || i%10==0){
             continue;
         }else{
             list.add(i);
         }
     }

     int c;
     for(int i=0;i<list.size();i++){
         c=0;
        for(int j=4;j<li.size();j++){
               if(li.get(j)>(int)Math.sqrt(list.get(i))){
                   break;
               }
            if(list.get(i)%li.get(j)==0){
                c++;
                break;
            }else{
                continue;
            }
        }
        if(c==0){
            li.add(list.get(i));
        } 
     }

     System.out.println(list.size());
     System.out.println(li.size());

     if(li.size()%2==0){
         return "Bob";
     } 
     else{
         return "Alice";
     }   
}

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;
}

JavaScript Solution

let ans = 0
    if (n === 1) return "Bob"
    else ans++      // because n>0
    function isPrime(i) {
// optimal the loop condition
        let limit = Math.round(Math.sqrt(i)) 
        for (let mod = 2; mod <= limit; mod++) {
            if (i % mod === 0) {
                return false;
            }
        }
        return true
    }
// eleminate the even number except 2 to optimal the loop
    for (let i = 3; i <= n; i += 2) {   
        if (isPrime(i))
            ans++
    }
    return ans % 2 === 0 ? "Bob" : "Alice"

Here is Alice and Bob's Silly game problem solution - https://programs.programmingoneonone.com/2021/07/hackerrank-alice-and-bobs-silly-game-problem-solution.html

Linear Sieve+Prefix Sums

void sive(){
	memset(lp,0,sizeof lp);
	for (int i=2; i<=N; ++i) {
	if (lp[i] == 0) {
		lp[i] = i;
		pr.push_back (i);
	}
	for (int j=0; j<(int)pr.size() && pr[j]<=lp[i] && i*pr[j]<=N; ++j){
		lp[i * pr[j]] = pr[j];
	}
    }
    a[0]=a[1]=0;
    for(int i=2;i<mxn;i++){
        if(lp[i]==i){
            a[i]=a[i-1]+1;
            continue;
        }
        a[i]=a[i-1];
    }
}
void test_case(){
	int n,cnt=0;
	read(n);
	if(n<2){
		cout<<"Bob"<<endl;
		return;
	}
	cnt=a[n];
	cout<<(cnt&1?"Alice":"Bob")<<endl;
}
int main(){
	int tt;
    sync();
	read(tt);
	sive();
	while(tt--){
		test_case();
	}
}