Divisor 4019
- Prime Number:
- Yes!
- Divisibility test:
- The "Paolo Franchi Test"
- Test Discovered by:
- Matt Parker
- Date:
- 11/11/2024
The "Paolo Franchi Test" for Divisibility by 4019
To determine if any number is divisible by 4019, apply the "Paolo Franchi Test":
- 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.
- Multiply L by 458 and add to R.
- Take that result and cross off its final digit (units). Take this new number and add 402 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 4019. That is, your original number is divisible by 4019 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 4019-times tables, it should be easy to visually see if Y is divisible by 4019. If the Y is still much larger than 4019, the above process can be repeated until it does reduce to within small multiples of 4019.
Easy!