Ah you're correct. Annoying how Google interprets log(x) as base-10 (but more shame on me for not realising that e^5 is obviously not 100000). In my experience everyone uses log and ln interchangeable outside of lessons at school.

log(x) historically conventionally defaults to base-10. https://en.m.wikipedia.org/wiki/Common_logarithm

As the wiki page itself notes though:

> On calculators, it is printed as "log", but mathematicians usually mean natural logarithm (logarithm with base e ≈ 2.71828) rather than common logarithm when they write "log".

Hi, can you provide some search terms that will help me understand the relationship between ln and prime density?

Or https://en.wikipedia.org/wiki/Prime-counting_function .

And you can knock out multiples of 3 by adding digits.

Sure, but that's a little more work than just looking at the last digit, so it's debatable whether it's worth the trouble.