Divisor 4003

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

The "Filip Sowa Test" for Divisibility by 4003

To determine if any number is divisible by 4003, apply the "Filip Sowa 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 75 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and add 1201 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 4003. That is, your original number is divisible by 4003 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 4003-times tables, it should be easy to visually see if Y is divisible by 4003. If the Y is still much larger than 4003, the above process can be repeated until it does reduce to within small multiples of 4003.

Easy!