Muncey Analysis

After calculating prime magic constants, I have wondered: how Muncey had build that square?
So I have try to analyze his square.

In the first step, I have converted the prime square into the normal correspondent square:
Substitute all the prime with it's index, e.g. calculate the P^-1() of the prime:

             1 143 142 140 141 139   8  10  65  11   9  12   821
            24  23  47  22 116 115 114 127 113  16  14 131   862
            25  49  27  28  44 102 128 129 111  34 134  60   871
            48 119  95  45  29  30 103  92  40 135 107  37   880
            73  75  98  76  53  91  55  56  57  39 110 109   892
            70  72  71 118  77  67  66  64  80  63  62  87   897
            96  99  51  68 101  78  82   7  79  58  83  84   886
            50  94  74  93  89  54  86  90  33  85  88  61   897
            97  46  21 100  69  43  42 104 106 105  38 108   879
           121  26 117  52 125 126  31  32  41 112  59  36   878
           120 122 123 124  20  19  18  15  17 132 130  13   853
           144   2   4   3   6   5 138 136 137  81  35 133   824

     872   869 870 870 869 870 869 871 862 879 871 869 871   869

Ho, no. I was thought that Muncey builds normal magic squares, until he founds a valid correspondent prime magic square, but how you can see the magic constant 870 for order 12 appears only in 3 columns.

So, analyze the last square with this technique: order all columns in ascendant order:

           1    2    4    3    6    5    8    7   17   11    9   12
          24   23   21   22   20   19   18   10   33   16   14   13
          25   26   27   28   29   30   31   15   40   34   35   36
          48   46   47   45   44   43   42   32   41   39   38   37
          50   49   51   52   53   54   55   56   57   58   59   60
          70   72   71   68   69   67   66   64   65   63   62   61
          73   75   74   76   77   78   82   90   79   81   83   84
          96   94   95   93   89   91   86   92   80   85   88   87
          97   99   98  100  101  102  103  104  106  105  107  108
         120  119  117  118  116  115  114  127  111  112  110  109
         121  122  123  124  125  126  128  129  113  132  130  131
         144  143  142  140  141  139  138  136  137  135  134  133

Well, we see something of interesting:

The first 12 numbers appear in the first line
The 13..24 appear in second, and so on
Only 17, 15 and 90 are in the expected line of 10, 33 and 80
The numbers are in increasing line ordered (with some exception) from sx to dx, then dx to sx, and so on like in a snake.

Ok. But what we can say if we use that analysis to row? (order all row in ascendant order)
Nothing that could have used for find something of useful.

However, using the preceding information I have been able to build my squares and probably I found the method that Muncey had used.
The method was not completely found in 1996, because stayed still from clarify a point about diagonals. In 1999 working with order 124, I have an hypothesis for the solution of that problem. So The Muncey Construction will be present only at the end of this work.

Magic Square

Tognon Stefano Research