Divisor 19391
- Prime Number:
- Yes!
- Divisibility test:
- The "Benjamin Smith Test"
- Test Discovered by:
- Matt Parker
- Date:
- 11/11/2024
The "Benjamin Smith Test" for Divisibility by 19391
To determine if any number is divisible by 19391, apply the "Benjamin Smith Test":
- If your number ("X") has 9 digits or more, separate the last (smallest) 8 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 9 digits, L = 0 and therefore R = X.
- Multiply L by 613 and add to R.
- Take that result and cross off its final digit (units). Take this new number and subtract 1939 times the digit you just crossed off. Call this final result "Y".
- Y will be much smaller than X, but we have preserved divisibility by 19391. That is, your original number is divisible by 19391 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 19391-times tables, it should be easy to visually see if Y is divisible by 19391. If the Y is still much larger than 19391, the above process can be repeated until it does reduce to within small multiples of 19391.
Easy!