Verifying a South African ID I'm verifying South African IDs with jQuery, the code below works but Id like to know if it could be simplified in anyway or if there is a better way of doing things here?

South African IDs are verified as follows:


Using ID Number 8001015009087 as an example:
Add all the digits in the odd positions (excluding last digit).
8 + 0 + 0 + 5 + 0 + 0 = 13  .............................[1]

Move the even positions into a field and multiply the number by 2.
011098 x 2 = 22196  .....................................[2]

Add the digits of the result in [2].
2 + 2 + 1 + 9 + 6 = 20  .................................[3]

Add the answer in [3] to the answer in [1].
13 + 20 = 33  ...........................................[4]

Subtract the second digit of [4](i.e. 3) from 10. The number must tally with 
the last number in the ID Number. If the result is 2 digits, the last digit is 
used to compare against the last number in the ID Number. If the answer differs, 
the ID number is invalid.



And the code:

var me = $("#id");
var odd = new Number();
var even_string = new String();
var even_result = new Number();
var even = new Number();
var result = new Number();

// Check length
if( me.val().length == 13 )
{
    $.each(me.val(), function(p,v){
        if (p%2 == 0 &amp; p != 12)
        {
            odd += Number(v); // --&gt; 1. Add all odd positions except the last one.
        }
        else
        {
            if(p != 12)
            {
                even_string += String(v); // --&gt; 2.1 Join all even positions.
            }
        }
    });

    // 2.2 Multiply even string by two.
    even_result = (even_string * 2);

    // 3. Add the digits of the new even result in two point two.
    $.each(String(even_result), function(p,v){
        even += Number(v);
    });

    // 4. Add answer in three to the answer in one.
    result = odd+even;

    // 5. Subtract the second digit from step 4. from ten.
    result = 10 - Number(String(result).substr(1,1));

    // 6. Make sure we use the very last digit on the result.
    if( (String(result)).length &gt; 1 )
    {
        result = Number( (String(result)).charAt( (String(result)).length-1 ) );
    }

    // 6. The final check
    if( Number(result) != me.val().substr(12,1) )
    {
        // Not a valid South African ID
        alert("Your South African ID is not valid.");
    }
};
jQuery is entirely unnecessary and will just make your solution slower
Don't initialize to new Class() - this is not Java. Instead, initialize to the initial value, or undefined (var x;).
use a function to encapsulate your verification logic, and to separate it from the DOM interface.
don't call me.val() more than once; cache the result
instead of the slow $.each, use a simpler loop
You already know the length of the id string, so you can get rid of the p%2 check and simply operate twice on each loop, once on the current position and once on p + 1, and increment by 2 each time (this also results in half as many iterations, speeding up the loop even further).
Cast using +string (resulting in a number) and '' + number (resulting in a string)
split the string into the first 12 and the last 1 at the beginning, so you don't have to keep excluding the last character and re-extracting it.
'string'.slice(-1) is a more concise way to access the last character in a string
check to make sure that not only is the string 13 characters long, but also that every character is a numeral


With all that and a few stylistic preferences, here's my take on your problem:

function isValidSAID(id) {
    var i, c,
        even = '',
        sum = 0,
        check = id.slice(-1);

    if (id.length != 13 || id.match(/\D/)) {
        return false;
    }
    id = id.substr(0, id.length - 1);
    for (i = 0; c = id.charAt(i); i += 2) {
        sum += +c;
        even += id.charAt(i + 1);
    }
    even = '' + even * 2;
    for (i = 0; c = even.charAt(i); i++) {
        sum += +c;
    }
    sum = 10 - ('' + sum).charAt(1);
    return ('' + sum).slice(-1) == check;
}

if (!isValidSAID(document.getElementById('id').innerHTML)) {
    alert('Your South African ID is not valid.');
}