Block-Bordered Magic Squares of Prime and Double Prime Orders: I, II and III

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:

  1. 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
  2. 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
  3. 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:

  1. https://inderjtaneja.com/2018/01/10/block-wise-magic-and-bimagic-squares-part-i/
  2. https://inderjtaneja.com/2018/01/10/block-wise-magic-and-bimagic-squares-part-ii/
  3. 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:

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:

  • Block-bordered magic squares of order 17
  • Block-bordered magic squares of order 23

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