Divisor 3911

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

The "Michał Bartoszkiewicz Test" for Divisibility by 3911

To determine if any number is divisible by 3911, apply the "Michał Bartoszkiewicz Test":

  1. If your number ("X") has 10 digits or more, separate the last (smallest) 9 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 10 digits, L = 0 and therefore R = X.
  2. Multiply L by 321 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 391 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 3911. That is, your original number is divisible by 3911 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 3911-times tables, it should be easy to visually see if Y is divisible by 3911. If the Y is still much larger than 3911, the above process can be repeated until it does reduce to within small multiples of 3911.

Easy!