This was a pretty easy hypothesis to test: I asked Gemini to generate 1000000 base-64 random characters (which is 20x more characters than it's output token limit).

It wrote code and outputted a file of length 1000000 and with 6 bits of entropy.

You can probably ask for a longer stringand do a better statistical test if it isn't convincing enough for you, but I'm pretty convinced.

Transcript: https://g.co/gemini/share/1eae0a4bb3db