Thanks for your reply, B.Diddy.
The numbers are indeed a combo of date and time.
Here's typical: 20160425_105709.jpg
And in the 'Date modified' column it shows '25/04/2016 10:57, so I assume I took the photo 9 seconds after 10:57.
So it's not possible to have the pics auto renumbered? No BFD, if not.
Say, are you an expert on the Galaxy Tab S 10.5? I've been trying to find out if I could somehow arrange to take photos in RAW format instead of JPG. No-one (including Samsung Help) seems to know if this is possible, either natively or with an app. I asked someone at 'A Better Camera' if their app would do it and got an incomprehensible reply which basically said 'No' and referred to 'debugging'.
Any ideas?