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

[PeterP]

Thank you Valentin for your kind help, yet to my embarrassment I am still confused.

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.`

In another post (apologies for cheating) someone listed the first perfect prime according to their analysis to be 294001.

Now, let me change a single digit and diminish its primeness by turning it into a composite number

294003 which is not prime as it is divisible by 3.

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.

Maybe someone can help me understand how 294001 is a perfect prime (or give me any perfect prime and help me understand how and why it is a perfect prime and can’t be made composite by changing any single digit.

Thank you so much for your indulgence in helping me understand!