Find Deletable Primes (LTT Problem solving 1)

import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;

public class DeletablePrimes {
    public static void main(String[] args){
        List<Integer> primes = primes(10000000);
        List<Integer> deletablePrimes = new ArrayList<Integer>();
        long sum = 0;
        for(int i : primes){
            if(isDeletablePrime(Integer.toString(i))){
                deletablePrimes.add(i);
                sum+=i;
            }
        }
        System.out.println(deletablePrimes.size());
        System.out.println(sum);
    }
    public static List<Integer> primes(int n){
        int p = 2;
        boolean[] primes_b = new boolean[n];
        Arrays.fill(primes_b, true);
        primes_b[0] = false;
        primes_b[1] = false;
        outerloop: while(p<n){
            for(int x=2; p*x<n;x++){
                primes_b[x*p] = false;
            }
            for(int i = 2; i<=primes_b.length;i++){
                //selecting next p
                try{
                    if(primes_b[i]){if(i>p){p=i;break;}}
                }catch(IndexOutOfBoundsException e){
                    break outerloop;
                }
            }
        }
        List<Integer> primes = new ArrayList<Integer>();
        for(int i =0;i<primes_b.length;i++){
            if(primes_b[i]){primes.add(i);};
        }
        return primes;
    }
    public static boolean isprime(int num){
        if(num < 2) return false;
        if(num == 2 || num == 3) return true;
        if(num%2 == 0 || num%3 == 0) return false;
        long sqrtN = (long)Math.sqrt(num)+1;
        for(long i = 6L; i <= sqrtN; i += 6) {
            if(num%(i-1) == 0 || num%(i+1) == 0) return false;
        }
        return true;
    }
    public static boolean isDeletablePrime(String prime){
        if(Integer.parseInt(prime.substring(0,1))==0){return false;};
        if(prime.length()==1){
            if(isprime(Integer.parseInt(prime))){
                return true;
            }else{
                return false;
            }
        }
        for(int r = 0; r<prime.length();r++){
            String buffer = prime.substring(0,r)+prime.substring(r+1,prime.length());
            if(isprime(Integer.parseInt(buffer))){
                if(isDeletablePrime(buffer)){
                    return true;
                }
            }
        }
        return false;
    }
}