Divisor 25903

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

The "Adric Test" for Divisibility by 25903

To determine if any number is divisible by 25903, apply the "Adric 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 1442 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and add 7771 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 25903. That is, your original number is divisible by 25903 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 25903-times tables, it should be easy to visually see if Y is divisible by 25903. If the Y is still much larger than 25903, the above process can be repeated until it does reduce to within small multiples of 25903.

Easy!