Divisor 13003

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

The "Przemek Zdunek Test" for Divisibility by 13003

To determine if any number is divisible by 13003, apply the "Przemek Zdunek 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 693 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and add 3901 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 13003. That is, your original number is divisible by 13003 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 13003-times tables, it should be easy to visually see if Y is divisible by 13003. If the Y is still much larger than 13003, the above process can be repeated until it does reduce to within small multiples of 13003.

Easy!