Divisor 25031

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

The "AB Test" for Divisibility by 25031

To determine if any number is divisible by 25031, apply the "AB Test":

  1. If your number ("X") has 6 digits or more, separate the last (smallest) 5 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 6 digits, L = 0 and therefore R = X.
  2. Multiply L by 124 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 2503 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 25031. That is, your original number is divisible by 25031 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 25031-times tables, it should be easy to visually see if Y is divisible by 25031. If the Y is still much larger than 25031, the above process can be repeated until it does reduce to within small multiples of 25031.

Easy!