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 **prime** and **double prime** orders. We call it as **block-bordered magic squares**. The work below is a combination of author’s following three papers:

- Inder J. Taneja, Block-Bordered Magic Squares of Prime and Double Prime Numbers – I,
**Zenodo**, August 18, 2020, pp. 1- 81, http://doi.org/10.5281/zenodo.3990291 - Inder J. Taneja, Block-Bordered Magic Squares of Prime and Double Prime Numbers – II,
**Zenodo**, August 18, 2020, pp. 1-90, http://doi.org/10.5281/zenodo.3990293 - Inder J. Taneja, Block-Bordered Magic Squares of Prime and Double Prime Numbers – III,
**Zenodo**, September 01, 2020, pp.1-93 http://doi.org/10.5281/zenodo.4011213

The bordered magic squares considered in this work are of orders 10 to 53.

- The
**first paper**works with orders: 10, 11, 13,1 7, 19, 22, 23, 26, 29, 31 and 34; - The
**second paper**works with orders: 34, 37 and 38; - The
**third paper**works with orders: 41, 43, 46, 47 and 53.

In order to bring these **block-bordered** magic squares, we make use of author’s previous works on **block-wise magics squares** of orders: 8, 9, 12, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32, 35, 36, 39, 40, 42, 44 , 45, 49 and 51. These block-wise magic square can be seen at the following links:

- https://inderjtaneja.com/2018/01/10/block-wise-magic-and-bimagic-squares-part-i/
- https://inderjtaneja.com/2018/01/10/block-wise-magic-and-bimagic-squares-part-ii/
- https://inderjtaneja.com/2018/03/02/block-wise-construction-of-magic-and-bimagic-squares-of-orders-39-to-45/

All the above work is done manually without use of any programming language, except the bordered magic squares. The bordered magic squares considred are by use softwhere due to **H. White**. See the links below:

- H. WHITE, Magic Squares – http://budshaw.ca/BorderedMagicSquares.html
- H. WHITE, Magic Squares – http://budshaw.ca/Download.html

Below are details of block-bordered magic squares appearing in all the three papers. The last image give idea of next work, i.e., 4th paper:

Below are few examples of **block-bordered** magic squares of orders 17 and 21 i.e., Results 5 and 23:

**B****lock-bordered**magic squares of order 17

**Block-bordered magic squares of order 23**

## 31 comments