Divisor 22303

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

The "Mike Thomson Test" for Divisibility by 22303

To determine if any number is divisible by 22303, apply the "Mike Thomson Test":

  1. If your number ("X") has 10 digits or more, separate the last (smallest) 9 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 10 digits, L = 0 and therefore R = X.
  2. Multiply L by 389 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and add 6691 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 22303. That is, your original number is divisible by 22303 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 22303-times tables, it should be easy to visually see if Y is divisible by 22303. If the Y is still much larger than 22303, the above process can be repeated until it does reduce to within small multiples of 22303.

Easy!