personnummer_validate.js

var validatePnr = function(str) {
  if(str.length != 12)
    return false;

  var date_string = [str.slice(0,4),'-',str.slice(4,6),'-',str.slice(6,8)].join('');

  if(isNaN(Date.parse(date_string)))
    return false;

  str = str.slice(2,12);
  var sum = 0
  numbers = str.split('').map(function(n){ return parseInt(n)});
  numbers.forEach(function(n, index){
    if(index % 2 == 0) n *= 2;
    if(n >= 10) n -= 9
    sum += n
  });
  return sum % 10 == 0
}

Use this polyfill if not using ES6 for forEach funtionallity.
https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/forEach