Divisor 5351

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

The "Pellevrault Sébastien Test" for Divisibility by 5351

To determine if any number is divisible by 5351, apply the "Pellevrault Sébastien 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 231 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 535 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 5351. That is, your original number is divisible by 5351 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 5351-times tables, it should be easy to visually see if Y is divisible by 5351. If the Y is still much larger than 5351, the above process can be repeated until it does reduce to within small multiples of 5351.

Easy!