The max safe integer representation in js is a Happy Number :) . Number.MAX_SAFE_INTEGER

happyNumbers

var myHN = function (){

    var  happyClosure = function(number){

        //started at
        var timeStamp = new Date().getTime();
      
        //save original number
        var happyNumber = number;
        //iterations done
        var iterNumber = 0;

        //create digits' array  from the given number
        var convertStr2Array = function(number){
            return Array.prototype.slice.call(number.toString(),function(digit){
                return Number(digit);
            });
        }
        
        // test if the string has a binary structure
        // if is like a binary string then number is a happy number
        var isBinaryString = function(number) {
            return /^[1]+[0]*$/.test(number);
        };

        //return the sum of squares
        var sumAll = function (arrStr) {
            var sum =0;
            for (var i = 0; i < arrStr.length; i++) {
                sum += Math.pow(arrStr[i], 2);
            }
            return sum;
        };

        return function(){
            var rightNow = new Date().getTime();
            var secs = (rightNow - timeStamp)/1000;
            if ( secs <= 5 && ( (iterNumber++) !== 299999) ){
                number = sumAll(convertStr2Array(number));
                if (isBinaryString(number) ){
                    //enough, is a happy number
                    return {'isHappyNumber':true , 'mayIContinue':false};
                }
            }else{
                var sadNumber = happyNumber;
                console.log("The time is up (%d iterations done)."+
                            " The elapsed time is %d secs"+
                            " I can't know if %d is happy or sad... :(  "
                , iterNumber, secs, sadNumber);
                return {'isHappyNumber':false, 'mayIContinue':false};
            }
            return {'isHappyNumber':false,'mayIContinue':true};
        };
    }

    var closure = happyClosure(arguments[0]);
    if (typeof closure === 'function'){
        do{
            var result = closure();
        }
        while(result.mayIContinue);
    }

    return result.isHappyNumber;
};

console.log("Max safely represented integer in js " + Number.MAX_SAFE_INTEGER +" is a Happy number :) " + myHN(Number.MAX_SAFE_INTEGER) );

create function myHN to calculate if a number is happy. Abort the mission after 300000 iterations or 5 seconds elapsed whatever comes first.

Use a closure to wrap in its own scope each calculation.