It can do: https://chat.openai.com/share/f1c0726f-294d-447d-a3b3-f664dc...

IMO the main reason it's distinguishable is because it keeps explicitly telling you it's an AI.

This isn't the same thing. This is a commanded recital of a lack of capability, not that its confidence in it's answer is low. For a type of question the GPT _could_ answer, most of the time it _will_ answer, regardless of accuracy

I just noticed that when I ask difficult technical questions, but for which there is an exact answer, he often tries to answer plausibly, but incorrectly instead of answering "I don't know".

Have you tried setting a custom instruction in settings? I find that setting helps, albeit with weaker impact than the prompt itself.

It's not a problem for me. It's good that I can detect chatGPT by this sign.

It doesn't become smarter except for releases of new models. It's an inference engine.

I read an article where they did a proper Turing test and it seems people recognize it was a machine answering because it made no writing errors and wrote perfectly

I've not read that, but I do remember hearing that the first human to fail the Turing test did so because they seemed to know far too much minutiae about Star Trek.

Maybe It's because It was never rewarded for such answers when It was learning.

Of course it does.

It absolutely does that (GPT-4 especially), and I have hit it many times in regular conversations without specifically asking for it.