The building being constructed in Downtown Raleigh near Moore Square Middle School that takes up the full city block of Martin Street, Bloodworth Street, East Street, and Hargett Street is a project called The Lincoln Apartments. The plans call for 224 residential apartment units ready for occupancy in the summer of 2015.
This block was cleared several years ago in preparation for development. Here is the Google Maps street view where you can see how this block looked in May 2013.