Divisor 22783

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

The "PhotonBurst Test" for Divisibility by 22783

To determine if any number is divisible by 22783, apply the "PhotonBurst Test":

  1. If your number ("X") has 8 digits or more, separate the last (smallest) 7 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 8 digits, L = 0 and therefore R = X.
  2. Multiply L by 1737 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and add 6835 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 22783. That is, your original number is divisible by 22783 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 22783-times tables, it should be easy to visually see if Y is divisible by 22783. If the Y is still much larger than 22783, the above process can be repeated until it does reduce to within small multiples of 22783.

Easy!