I think the general prime day deals on new stuff are a bit hit and miss - it's all very well discounting a set of pans by 30% but most people would only buy something like this every few years. If you want "a big telly" and aren't too fussy then there can be some good deals.
For the last couple of years I've done OK from the 20% off Amazon Warehouse offer. Amazon warehouse is where they sell returned stuff, but the discounts are usually very poor so the extra 20% off makes it interesting. You have to be careful what you're buying (they will tell you if there's accessories missing and what condition it's all in) but there's some good savings in there. I filled my basket up with stuff from the warehouse yesterday afternoon and set my alarm for 11.58pm knowing that the 20% offer might start at midnight - sure enough it did. But even though I checked out just after midnight, a couple of items were bought from under me by other equally sad people.
Rumour has it that you can avoid this happening by buying the items at normal warehouse price before midnight and then quickly cancel and re-order with 20% off at your leisure before they despatch.
As advised above, always check a price tracker and also other websites because sometimes stuff is cheaper elsewhere even with the offers. eBay for example are running a 20% off code at the moment to compete with Amazon. Only works with selected sellers this time but I bought a couple of things from there yesterday rather than waiting for Amazon because it was cheaper.