Divisor 20717

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

The "Sebastian Koch Test" for Divisibility by 20717

To determine if any number is divisible by 20717, apply the "Sebastian Koch 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 959 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 6215 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 20717. That is, your original number is divisible by 20717 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 20717-times tables, it should be easy to visually see if Y is divisible by 20717. If the Y is still much larger than 20717, the above process can be repeated until it does reduce to within small multiples of 20717.

Easy!