Divisor 9007

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

The "Allan Lindqvist Test" for Divisibility by 9007

To determine if any number is divisible by 9007, apply the "Allan Lindqvist Test":

  1. If your number ("X") has 7 digits or more, separate the last (smallest) 6 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 7 digits, L = 0 and therefore R = X.
  2. Multiply L by 223 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 2702 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 9007. That is, your original number is divisible by 9007 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 9007-times tables, it should be easy to visually see if Y is divisible by 9007. If the Y is still much larger than 9007, the above process can be repeated until it does reduce to within small multiples of 9007.

Easy!