I have been having a lot of trouble finding a digital clock. I don't even know where to ask for recs, I tried a couple subreddits but there is no /r/digitalclocks so I'm trying a more general place here and maybe someone can help?

My requirements (I'm in the USA so that's where the time finding needs to happen):

1. It autosets the time based on the radio signal
2. It automatically detects DST
3. Backup battery so if I get a power failure it doesn't lose the time
4. The time is the only thing on the display. (Although, this seems to be the hardest one to find, so, if it also shows the temperature or something, that's ok, as long as the time is a lot bigger than anything else)
5. Not willing to spend more than $50 on a clock
6. Needs to be LED not LCD, i.e. I want to be able to see the time in a dark room without pressing a light-up button or anything

Additional bonuses:

1. If it has a rainbow display
2. If it has a USB charging port
3. Big numbers, like at least 1.5" tall

I don't care about the alarm or any overhead projection features.

If you have a digital clock that you love that meets these requirements (or at least mostly does) I would like to hear about it!! Thanks!!

I bought a Timex Expedition North Titanium Automatic a few months ago and have been enjoying it, but it gains about 10s a day that I have to correct. Nowadays we have incredibly accurate and precise clocks that can tell us exactly what time it is, but all mechanical clocks and watches have some amount of inaccuracy.

How did people account for inaccurate clocks in the past? Even if time didn't need to be standardized outside of a community until the railroads and a central clock in town could act as a reference for the entire community, wouldn't the central community clock drift? Eventually the central clock could say it was midnight at sunset. While people can tell that is incorrect, how could they say to what extent it was incorrect?