Divisor 16903

Prime Number:
Yes!
Divisibility test:
The "Markus Dunphy-Knutsson Test"
Test Discovered by:
Matt Parker
Date:
11/11/2024

The "Markus Dunphy-Knutsson Test" for Divisibility by 16903

To determine if any number is divisible by 16903, apply the "Markus Dunphy-Knutsson Test":

  1. If your number ("X") has 11 digits or more, separate the last (smallest) 10 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 11 digits, L = 0 and therefore R = X.
  2. Multiply L by 733 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and add 5071 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 16903. That is, your original number is divisible by 16903 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 16903-times tables, it should be easy to visually see if Y is divisible by 16903. If the Y is still much larger than 16903, the above process can be repeated until it does reduce to within small multiples of 16903.

Easy!