Divisor 1997

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

The "Robert Wilson Test" for Divisibility by 1997

To determine if any number is divisible by 1997, apply the "Robert Wilson Test":

  1. If your number ("X") has 5 digits or more, separate the last (smallest) 4 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 5 digits, L = 0 and therefore R = X.
  2. Multiply L by 15 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 599 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 1997. That is, your original number is divisible by 1997 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 1997-times tables, it should be easy to visually see if Y is divisible by 1997. If the Y is still much larger than 1997, the above process can be repeated until it does reduce to within small multiples of 1997.

Easy!