I know a lot of you are complaining about the update taking a long time on PS4. I know I had this issue to. I got so fed up with it so I contacted Sony they told me to run a wired connection to my PS4 and reset my router. So far this has worked for me. This is a 6GB update so it can take up to 6 hours on a basic 3mbps network. Also don't blame Bungie for the slow download. The patch is Downloaded through the PS store not through Bungie's servers so Bungie can't do anything about it.
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Mine gets to 5.696 GB and then drops back to 5.652...and then says "cannot download file" multiple times now... WTF BUNGIE?!