Prime 17 is a prime number, because it has exactly 3 distinct prime factors: 1, 17, and 1.
But, you ask, what's the algorithmic justification for this prime number?
Well, my friend, it's simple: 17 is prime because it's the number of related prime factors of 29.
Related Prime 23 has a different algorithmic justification.
But, if you want to get really deep, Related Prime 23 has a related factor of 29!