Divisor 21503

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

The "Simon Job Test" for Divisibility by 21503

To determine if any number is divisible by 21503, apply the "Simon Job 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 1105 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and add 6451 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 21503. That is, your original number is divisible by 21503 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 21503-times tables, it should be easy to visually see if Y is divisible by 21503. If the Y is still much larger than 21503, the above process can be repeated until it does reduce to within small multiples of 21503.

Easy!