On my ti84+ the year can only be set later than 1996 and earlier than 2133. Any reason for this? Why these particular years as bookends? They seem fairly arbitrary to me.

Silly question I know but I'm genuinely curious.

The earlier date is an arbitrary engineering decision with no particular significance, other than that the TI-83 series was being developed at that time, so it's possible they recycled some code from that time that just happens to not support dates earlier than 1996. The 2133 limit comes from the fact that the TI-84+'s clock circuit stores the time as the number of seconds after some particular date, known as the epoch. Specifically, it uses a standard 32-bit unsigned dword, giving it a range of 2^32 seconds, which is 136 years plus a month or two.

So, 1996 is an arbitrary start date that they effectively just picked out of a hat, and 2133 comes from the fact that the clock circuit only supports a range of a little over 136 years.

And yes, the operating system could be reprogrammed to support a different epoch, and the clock circuit would still work just fine. That said, there is not likely to be much advantage to doing so.

Yes, it seems that log2(136 * 365.25 * 24 * 3600) = 31.998946995992030991749016334675. Indeed, a 32-bit integer.

Thanks for the clarifying responses. Glad I can put that question to rest.

An interesting fact though is while the clock cannot be easily set past 12/31/2132, it will keep counting! (Though I don't know how far or what will happen, just that I have observed it continue ticking after 4291746200s after 0s... I wonder if it overflowed or not...)

The clock will, in fact, overflow eventually. The overflow should happen in early February of 2133. Upon overflow, it should reset to the start of the epoch, which would be 1997.

Could the OS possibly be patched so that it can use out-of-range dates?

I am only asking because I am curious.
It is obvious that no ti84+/se will EVER last until 2133, so there won't be a practical use for such a patch.

The clock hardware only supports a 32-bit data range. The OS's interpretation of those values can definitely be patched, but I see little advantage to doing so.

As far as I can tell, the primary limiter of calculator lifetime is the flash chip. Flash memory uses superinsulators to trap static electric charges storing data. Over the course of decades, those charges slowly fade away. Calculators manufactured after something like 2012 have their flash chip's boot sector hardware-locked, so you have no way to refresh boot sector data. Older TI-84+s, however, can have their boot sector reflashed. As long as you reflash the boot sector and OS every decade or so and don't put the archive through many garbage collect cycles, the calculator should last indefinitely. Newer calculators are likely to become unbootable after about 20 years. (The newer flash chips have shorter data retention specs. Older calculators may remain bootable, even without firmware refresh, for twice as long.)

Thanks for the info, but is there a way of figuring out which revision my calc is so that I can predict its lifespan? (My calc is a ti84+SE purchased in december 2009). Also, is it possible to put the start date a bit later so that the clock can be set to an even later date?

Not without modifying the OS

Is there a way to mod the OS?

Nope when trying it the calc resets.