Divisor 2591

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

The "Mr Moxie Test" for Divisibility by 2591

To determine if any number is divisible by 2591, apply the "Mr Moxie 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 126 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 259 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 2591. That is, your original number is divisible by 2591 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 2591-times tables, it should be easy to visually see if Y is divisible by 2591. If the Y is still much larger than 2591, the above process can be repeated until it does reduce to within small multiples of 2591.

Easy!