This seems to work well for me:

Tire width proportioned to rider weight

I've had no problems with flats since changing out the main tire.

This is excellent advice in general, but only you know where you ride, what the drivers and traffic are like, and how comfortable you are riding in the travel lane. You may not feel comfortable/safe riding away from the shoulder where most of the debris and, therefore, flat risk, is to be found.

To add to the "ride here to reduce the risk of flats" advice:
- in intersections, avoid the triangle between where people go straight and people turn right, that area tends to accumulate debris
- avoid riding through sand/dirt left behind by rain on the side of the road, debris gets washed there and, since the debris is supported by sand, it isn't always lying flat on the road, and this also increases the risk of a flat

Note that there is not necessarily something wrong with your rear tire. Most flats happen on the rear tire. It bears more of your weight, therefore greater chance of pinch flats, and debris can penetrate further into the tread because there is more weight. Also, debris tends to accumulate on the road flat with the sharp bits down - so, for example: a curved piece of glass from a beer bottle is usually tossed around until it ends up with the convex surface up/sharp points down, which is the most stable position because the sharp points dig into the pavement and resist forces trying to move the piece of glass around. Then, you ride over it with your front tire and, maybe, that tumbles the piece of debris and you run over it with your rear tire while the sharp bits are pointed up.