[VA] Short & Sweet Math Challenge #25 "San Valentin's Special: Weird Math"

[Werner]

(02-26-2021 07:31 AM)PeterP Wrote:  

Valentin Wrote:[...] consider a prime number so 'Perfectly Prime' (a PP for short, pronounced "Pepe") that changing any single digit would diminish its primeness by turning it into a composite number. Note: We're talking about base-10 digits here.`

Now, it is entirely possible that the posted solution of 294001 as a perfect prime is incorrect. But it seems to me that I could change a single digit of any prime number in such a way that the resulting number is divisible by 3. Which would mean there are no perfect primes.

Yes, you can change *a* single digit of any prime to make it divisible by 3.
In a perfect prime, however, you could change ANY digit, and it would not be prime anymore.

Take 11, for instance.
If you change its last digit to 2, it is no longer prime. But if you change it to 3, it IS prime, so 11 is not a perfect prime.
The goal is to find primes so that changing any digit would NOT result in another prime.

Cheers, Werner