gistfile1.js

var ans=0;
var primes=Array(1,1,1,1,2,3,5,7,11,13,17)
function dfs(k, bit, sum) {
  if((sum % 1000) % primes[k] != 0)return;
  if(k == 10){
    ans += sum;
  }else{
    for(var i = 0; i < 10; i++){
      if((bit >> i) &1)continue;
      dfs(k + 1, bit | (1<<i), sum * 10 + i);
    }
  }
}
dfs(0, 0, 0);
console.log(ans); // Output:16695334890