> Primes have no inherent relation to decimal, so all prime patterns in decimal are mathematically meaningful.

No. There's all sorts of random nonsense in all base expansions of anything that we assign meaning to. Most base-related stuff is numerology.

> P.S. never say "base 10", it's a tautology. Say "decimal"

No, it's not. You need to specify your base number.

I'm not certain, but I believe the subtle point parent was trying to make, is the difference between "base 10" and "base ten". Every base is "base 10" in its own base ;)

if "base 10" is a tautology, wouldn't that make "deci-mal" a tautology too?

so yeah, just hold up 10 fingers and don't say anything.

But numerals "10" in bases other than decimal aren't usually called ten, I think.

Ten is "decem" in Latin. Decimal means, literally, base ten. It's a tautology either way. You can't even specify the base of the base since "base (10 in base 10)" presents the same problem recursively.

It's a non-problem though. I don't know about mathematicians, but when programmers say base N they mean N in decimal.

EDIT: woops, replied to the wrong post.

"10" is never correctly called "ten" except in decimal. But this whole tangent is getting a little navel-gazey for me. "Base 10" is fine in my book because decimal is our inbuilt base.

That's what I said (or tried to :) ).

Should we call it "base a"?

"base ||||| |||||"

perhaps "base |||||*||", for short.

base X (romans)

base II*II+II?

I get the parent poster's point, but to me it's like quibbling over people using "comprised of" instead of "comprises": some people will care, but in the grand scheme of things it's not a meaningful disagreement because everybody got what you were trying to say the first time, and there are only a few rare contexts where the distinction matters.

Base (((((((((1++)++)++)++)++)++)++)++)++)

Peano would be proud.

> P.S. never say "base 10", it's a tautology.

If you actually believe this, you must be endlessly confused when people say "base 8".