[rickduggan]

It's not an unexpected property to me. In particular, I would never have assumed an even distribution of last digit of primes. I'm not sure why this is so magical. It's only so if you assumed it should be evenly distributed to begin with, and there's no particular reason I can think of why this would be so.

[waterhouse]

Then you might be surprised that it's a mathematical fact that the last digit of primes is evenly distributed (among digits coprime to the base), no matter what base you choose. This is one way of stating the Chebotarev density theorem:

https://en.wikipedia.org/wiki/Chebotarev%27s_density_theorem

(edit: rephrasing)

[m00n]

Cebotarev is a bit of overkill (and not equivalent!) for this and hard to grasp, if your Algebraic Number Theory is a bit rusty.

I recommend Dirichlet's Theorem on arithmetic progressions instead (everybody loves Euler's totient function!) :

https://en.wikipedia.org/wiki/Dirichlet's_theorem_on_arithme...

[rickduggan]

Believing that the last digit of primes is evenly distributed overall is not the same as thinking they do not exhibit patterns when viewed sequentially. I'm surprised by neither.