Anatomy of Credit Card Numbers

Anatomy of credit card numbers

Validation by Luhn Algorithm

Submitted by: Haris Karim

Class: 9-B

March 11, 2016

CAS SCHOOL

Project Submitted for Application of mathematics

Anatomy of Credit Card Numbers

Introduction

Mathematics is the queen of science and the language of nature. Its importance should be clear to any reasonable person. It is easy however to diminish the value of certain areas of research because they’re currently thought as having little practical use. Evolutionary needs brought our mind to prefer knowledge that can be employed for the solution of specific problems in the real world, rather than deeply abstract ones. It is an understandable that there are useful fields of math and useless ones, based on the perception of their applied or theoretical nature. But it’s still a misconception. Each theorem and discovery is a little piece of a larger puzzle. Discoveries and mathematical ideas that are perceived as “useful” today because they’re applicable to engineering, for example, were at a certain point in time considered absolutely abstract and useless. Therefore Mathematics matters; all of it.

Modulo Algebra at one time was considered to be abstract and useless branch of mathematics but today it is an important tool used for Cryptography and other check sum validation techniques used to validate the syntax of various formats such Credit Card Numbers, Account Numbers, Social Security numbers, etc.

The part of the Modulo Algebra use to validate Credit Card number is known as Luhn algorithm or Luhn formula, also known as the "modulus 10" or "mod 10" algorithm. The formula verifies a number against its included check digit, which is usually appended to a partial account number to generate the full account number.

Methodology

The number must pass the following test:

From the rightmost digit, which is the check digit, moving left, double the value of every second digit; if the product of this doubling operation is greater than 9...