Divisor 22511

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

The "Marc Barnholdt Test" for Divisibility by 22511

To determine if any number is divisible by 22511, apply the "Marc Barnholdt 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 5116 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 2251 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 22511. That is, your original number is divisible by 22511 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 22511-times tables, it should be easy to visually see if Y is divisible by 22511. If the Y is still much larger than 22511, the above process can be repeated until it does reduce to within small multiples of 22511.

Easy!