I learnt the hard way when my wheel punctured and I was about a mile from the car, walking through long grass with all my kit on after a night was not fun. I used to keep a pump in my under bag though so kept stopping to re-inflate every 250m. with a 4 mile walk you dont want to be stuck there with a puncture. forget the prestige puncture proof tyre, take the normal one to somewhere like B&Q or garden centre and see if they have a matching wheelbarrow tyre that's puncture proof. much cheaper.