JavaScript summing large integers

No. Javascript only has one numeric type. You've to code yourself or use a large integer library (and you cannot even overload arithmetic operators).

Update

This was true in 2010... now (2019) a BigInt library is being standardized and will most probably soon arrive natively in Javascript and it will be the second numeric type present (there are typed arrays, but - at least formally - values extracted from them are still double-precision floating point numbers).

BigInt is being added as a native feature of JavaScript.

typeof 123;
// → 'number'
typeof 123n;
// → 'bigint'

Example:

const max = BigInt(Number.MAX_SAFE_INTEGER);
const two = 2n;
const result = max + two;
console.log(result);
// → '9007199254740993'

JavaScript uses floating point internally.

What is JavaScript's highest integer value that a number can go to without losing precision?

In other words you can't use more than 53 bits. In some implementations you may be limited to 31.

Try storing the bits in more than one variable, use a string, or get a bignum library, or if you only need to deal with integers, a biginteger library.

javascript now has experimental support for BigInt.
At the time of writing only chrome supports this.

caniuse has no entry yet.

BigInt can be either used with a constructor, e.g. BigInt(20) or by appending n, e.g. 20n

Example:

const max = Number.MAX_SAFE_INTEGER;

console.log('javascript Number limit reached', max + 1 === max + 2) // true;

console.log('javascript BigInt limit reached', BigInt(max) + 1n === BigInt(max) + 2n); // false