Hey there!
So I somehow managed to remember this number-theory-ish concept that I came up with last year. It's just another kind of prime number, but it fascinated me, considering I thought I was the first one to think of it and that it was about my favorite subject at the time. Anyway, allow me to introduce to you the new kinds of primes I came up with: double and triple primes.
I'll start with double primes. For a number to be a double prime, it must already be a regular prime number, and its digits must sum to another prime number. This doesn't seem that complex, does it? Moving on to triple primes, we add a new criterion: every pair of digits in the number must be a prime as well. For example, is a triple prime because:
a) is a regular prime number,
b) the digits of add up to , another prime number, and
c) every pair of digits in (i.e., ) is another prime number.
What's special about is that it isn't just every pair reading from left to right that's a prime number. Actually, if you take any two distinct digits of next to each other either way to form another number, it will be a prime number. I remember I took it a step up looking for quadruple primes (i.e., the same as triple primes except every permutation of the digits must be a prime number as well), but I don't think I was really that successful. Anyway, I leave just one question to you: can you find any triple primes?