Published July 19, 2026 | Version v1

Higher-Order Block-Structured Prime Magic Squares: Multiples of Order 9

  • 1. Formerly, Professor of Mathematics, Federal University of Santa Catarina, Florianópols, SC, Brazil

Description

This work bring different ways of representing prime magic squares multiples of order 9. It is based on some central prime constants. These are C0:= 499979, C1:=1000003 and C2:=2000003. The multiple blocks are considered based on these prime constants. Two different types are considered. One type is concentric blocks of order 9, and the second type is different sums blocks of order 3. For each type there are four ways of representations. First, when all blocks are of equal size. Second, when the blocks are of orders 27, 36 and 45 composed of different sums concentric prime magic squares of order 9. To understand better few examples are given. Some initial works based  on block-structured and/or  block-bordered prime magic squares for the orders 6 to 51 are given by the author. See the reference list. The higher-order concentric single-layer bordered prime magic squares of orders 1222 and 1223 is also given by the author. A different work for prime magic squares of order 1220 multiples of equal sums blocks of order 4 is also given by the author. For higher order multiples of 3, 4, 5, 6, 7 and 8 refer author's work in reference list.

The complete excel sheets are attached with the work.

 

Files

Higher-Orders-9.pdf

Files (20.0 MB)

Name Size Download all
md5:0dc32c386de32b77dad1c6b2f96270ce
13.6 MB Preview Download
md5:1626598e36c48f74feca14caf1c2266c
3.2 MB Preview Download
md5:65b5d33bf5f221b5be5b37d341056cf2
3.1 MB Preview Download