Divisor 3593

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

The "Markus Test" for Divisibility by 3593

To determine if any number is divisible by 3593, apply the "Markus 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 167 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and add 1078 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 3593. That is, your original number is divisible by 3593 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 3593-times tables, it should be easy to visually see if Y is divisible by 3593. If the Y is still much larger than 3593, the above process can be repeated until it does reduce to within small multiples of 3593.

Easy!