Divisor 10729

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

The "Paul Walker Test" for Divisibility by 10729

To determine if any number is divisible by 10729, apply the "Paul Walker 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 572 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and add 1073 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 10729. That is, your original number is divisible by 10729 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 10729-times tables, it should be easy to visually see if Y is divisible by 10729. If the Y is still much larger than 10729, the above process can be repeated until it does reduce to within small multiples of 10729.

Easy!