Using the range of values for the compressive strength and density of high quality brick masonry, the answers come out in a range between 4653 and 5273 meters. This is for a solid tower the same width up its entire height.

This seems about right. The instinct for 'is this answer in the right order of magnitude?' is very useful. There's a different between a wrong answer, and a plain silly one.

The Chrysler building is brick on a steel frame, Bill.