Divisor 7937

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

The "Douglas Miller Test" for Divisibility by 7937

To determine if any number is divisible by 7937, apply the "Douglas Miller 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 62 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 2381 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 7937. That is, your original number is divisible by 7937 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 7937-times tables, it should be easy to visually see if Y is divisible by 7937. If the Y is still much larger than 7937, the above process can be repeated until it does reduce to within small multiples of 7937.

Easy!