We can always write block-wise magic squares of any order except for the orders of type p and 2p, where p is a prime number. On the other hand we can always write bordered magic squares of any order. The aims of this work is to combine bordered and \block-wise magic squares, for the magic squares of \textbf{prime} and \textbf{double prime numbers} orders. We call it as block-bordered magic squares. The magic squares considered in this work are of orders 10, 11, 13, 14, 17, 19, 22, 23, 26, 29 and 31. In order to bring these block-bordered magic squares, we make use of author's previous works on block-wise constructions of magics squares, such as, of orders, 8, 9, 12, 16, 18, 20, 21, 24, 25 and 27. The second part of this work is for the block-bordered magic squares of orders 34, 37 and 38 \cite{ta41}. The third part is for the magic squares of orders 41, 43, 46 and 47.