Can't be a surprise given the number of consoles pounding PSN.

Hope you guys downloaded that day one update to USB as per my post earlier.
http://ca.ign.com/articles/2013/11/1...ume-of-log-ons
Sony has urged fans to be patient while the US and Canadian PSN experiences issues following the launch of the PlayStation 4.
A number of new PlayStation 4 owners have contacted IGN saying they're encountering the error numbers NW-31453-6 or NP-3500-8, along with text explaining "The network connection has been lost".
If you're struggling to download the patch, you can always get it from PlayStation.com, put it on a USB stick, and use that to update the console.