What is the maximum number of telephone numbers that can be used under a single three-digit area code?

Theoretically, about 7.9 million.

The first digit of a local phone number in North America (country code +1 = USA, Canada, etc.) cannot be 0 or 1. The first three digits cannot coincide with short codes like 911 and 411, and usually cannot coincide with the area code or any adjacent area code.