Divisor 21589

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

The "Benjamin Richter Test" for Divisibility by 21589

To determine if any number is divisible by 21589, apply the "Benjamin Richter Test":

  1. If your number ("X") has 9 digits or more, separate the last (smallest) 8 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 9 digits, L = 0 and therefore R = X.
  2. Multiply L by 248 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and add 2159 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 21589. That is, your original number is divisible by 21589 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 21589-times tables, it should be easy to visually see if Y is divisible by 21589. If the Y is still much larger than 21589, the above process can be repeated until it does reduce to within small multiples of 21589.

Easy!