Check out Michelin Protek Max tires. I've run a set of 700x40 Protek Cross Max for a year without flats. Got sick of flats after four in one month last year with a lighter weight set of tires on our local rough roads.
Typical Texas roads: smooth and rough pavement and chipseal with lots of broken glass, roofing nails, drywall screws, shards of metal, goat head grass burrs, etc.
I inspected the rear tire a few days ago and found a couple of glass splinters embedded in the tread, but nothing punctured the thick puncture shield. I tweezed out the glass and filled the small cuts with Shoe Goo. Then I rotated the tires and put the less worn front on the back.
When I first installed the tires I checked them at least once a week and found no visible wear for months.
Thought I'd had my first flat last week after experiencing some slow leaks, but there was no puncture in the tube. My best guess was a slightly loose core in the Schrader stem, possibly from using a threaded chuck. I snugged up the valve core and refilled the tube. No problems or slow leaks.
They're heavy -- 1,100 gr for 40c. But they grip like Velcro and ride well on dry and wet pavement of all kinds, gravel trails, everything but climbing muddy hills. Suits my 12 mph overall average.