Divisor 9539

Prime Number:
Yes!
Divisibility test:
The "Mark Smith Test"
Test Discovered by:
Matt Parker
Date:
11/11/2024

The "Mark Smith Test" for Divisibility by 9539

To determine if any number is divisible by 9539, apply the "Mark Smith Test":

  1. If your number ("X") has 5 digits or more, separate the last (smallest) 4 digits from the rest. This makes two smaller numbers, call them Left and Right (note: don't add in trailing zeros to L). If there are fewer than 5 digits, L = 0 and therefore R = X.
  2. Multiply L by 461 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and add 954 times the digit you just crossed off. Call this final result "Y".
  4. Y will be much smaller than X, but we have preserved divisibility by 9539. That is, your original number is divisible by 9539 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 9539-times tables, it should be easy to visually see if Y is divisible by 9539. If the Y is still much larger than 9539, the above process can be repeated until it does reduce to within small multiples of 9539.

Easy!