This work bring different ways of representing prime magic squares. These are higher order prime magic squares multiples of orders 3 and 4. For each order, the work is done in done based on fixed central constants, such as C0:= 499979, C1:=1000003, C2:=2000003, C3:=3000017, etc. The multiple blocks are considered for these prime constants. First when all blocks are of equal size. Second, when the blocks of equal sums of orders 12, 15, 18, 21 and 24 considered. These are composed of different sums concentric prime magic squares of order 3. In case of order 4, the equal sums blocks of orders 12, 16, 20 and 24 are considered. Each block is composed of different sums concentric prime magic squares of order 4. To understand better few examples are given. The complete excel sheets are attached with the work. The initial work of type block-structured and block-bordered on prime magic squares for the orders 6 to 51 is given by the author. See the reference list. The higher order concentric single-layer bordered prime magic squares of orders 160 and 161 are also given by the author..The author also presented prime magic squares of order 1220 using the idea of equal sums blocks of order 4. The excel files of complete work are also attached.