Divisor 17011

Prime Number:
Yes!
Divisibility test:
The "Andy & Elaine Pickering Test"
Test Discovered by:
Matt Parker
Date:
11/11/2024

The "Andy & Elaine Pickering Test" for Divisibility by 17011

To determine if any number is divisible by 17011, apply the "Andy & Elaine Pickering Test":

  1. If your number ("X") has 11 digits or more, separate the last (smallest) 10 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 11 digits, L = 0 and therefore R = X.
  2. Multiply L by 1405 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 1701 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 17011. That is, your original number is divisible by 17011 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 17011-times tables, it should be easy to visually see if Y is divisible by 17011. If the Y is still much larger than 17011, the above process can be repeated until it does reduce to within small multiples of 17011.

Easy!