Divisor 6689

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

The "Torsten Velker Test" for Divisibility by 6689

To determine if any number is divisible by 6689, apply the "Torsten Velker Test":

  1. If your number ("X") has 8 digits or more, separate the last (smallest) 7 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 8 digits, L = 0 and therefore R = X.
  2. Multiply L by 55 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and add 669 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 6689. That is, your original number is divisible by 6689 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 6689-times tables, it should be easy to visually see if Y is divisible by 6689. If the Y is still much larger than 6689, the above process can be repeated until it does reduce to within small multiples of 6689.

Easy!