Divisor 10111

Prime Number:
Yes!
Divisibility test:
The "Harold De Armas Test"
Test Discovered by:
Matt Parker
Date:
11/11/2024

The "Harold De Armas Test" for Divisibility by 10111

To determine if any number is divisible by 10111, apply the "Harold De Armas 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 221 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 1011 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 10111. That is, your original number is divisible by 10111 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 10111-times tables, it should be easy to visually see if Y is divisible by 10111. If the Y is still much larger than 10111, the above process can be repeated until it does reduce to within small multiples of 10111.

Easy!