Office Applications and Entertainment, Magic Squares  
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14.0 Special Magic Squares, Prime Numbers
Sophie Germain Primes
{a_{i}} are prime numbers for which the operation
{b_{i}} = 2 * {a_{i}} + 1 results in prime numbers {b_{i}}
for i = 1 ... n.
Attachment 14.17.1
shows for the range {b_{i}} = (23 ... 174299) the first occurring
pairs of 3 x 3 Sophie Germain Magic Squares for miscellaneous Magic Sums.
Attachment 14.17.14
shows for the range {b_{i}} = (11 ... 1319) the first occurring
pairs of 4 x 4 Sophie Germain Simple Magic Squares for miscellaneous (smaller) Magic Sums
(ref. Priem4a).

MC4a = 21944
3779 3623 6899 7643 3761 10781 641 6761 4073 3329 7193 7349 10331 4211 7211 191 MC4b = 43892
7559 7247 13799 15287 7523 21563 1283 13523 8147 6659 14387 14699 20663 8423 14423 383
The pair shown corresponds with 384 pairs with the same Magic Sums and variable values {a_{i}}/{b_{i}}, i = 1 ... 16.
Attachment 14.17.3
shows for the range {b_{i}} = (23 ... 43607) the first occurring
pairs of 5 x 5 Sophie Germain Simple Magic Squares for miscellaneous Magic Sums.
Each pair shown corresponds with numerous pairs with the same Magic Sums and variable values {a_{i}}/{b_{i}}, i = 1 ... 25.
Attachment 14.17.9
shows for the range {b_{i}} = (23 ... 43607) the first occurring
pairs of 6 x 6 Sophie Germain Simple Magic Squares, with symmetrical main diagonals, for miscellaneous Magic Sums.

MC6a = 20946
6173 719 2039 2063 6329 3623 419 6899 431 1583 5051 6563 1901 131 6323 5171 2339 5081 3593 5003 1811 659 6491 3389 5501 1931 5399 6551 83 1481 3359 6263 4943 4919 653 809 MC6b = 41898
12347 1439 4079 4127 12659 7247 839 13799 863 3167 10103 13127 3803 263 12647 10343 4679 10163 7187 10007 3623 1319 12983 6779 11003 3863 10799 13103 167 2963 6719 12527 9887 9839 1307 1619
Attachment 14.17.10
shows for the range {b_{i}} = (23 ... 43607) the first occurring pairs of 6 x 6 Sophie Germain Bordered Magic Squares
for miscellaneous Magic Sums.
Attachment 14.17.11 shows a few examples of
pairs of 7 x 7 Sophie Germain Bordered Magic Squares, based on the
pairs of 5 x 5 Sophie Germain Simple Magic Squares as discussed in Section 14.17.3 above.
Attachment 14.17.15 shows a few examples of
pairs of 7 x 7 Sophie Germain Concentric Magic Squares, based on the
pairs of 5 x 5 Sophie Germain Concentric Magic Squares as discussed in Section 14.17.3 above.
Each pair shown corresponds with numerous pairs with the same Magic Sums and variable values {a_{i}}/{b_{i}}, i = 1 ... 49,
(Order of magnitude 8 * (5!)^{2} = 115200 for the Same Center Square).
14.17.6 Magic Squares, Composed (8 x 8)
In Section 14.6.1 was discussed how Prime Number Magic Squares of order 8  with Magic Sum 2 * s1  can be composed out of 4^{th} order Prime Number Magic Squares with Magic Sum s1.

MC8a = 43888
10883 911 2939 7211 8273 2819 7883 2969 1559 9371 7151 3863 683 10799 2393 8069 5741 3821 1601 10781 2459 6053 2699 10733 3761 7841 10253 89 10529 2273 8969 173 7349 281 6491 7823 3851 2549 6323 9221 1031 7643 4211 9059 8741 7121 1289 4793 6983 3329 6761 4871 4019 6101 7433 4391 6581 10691 4481 191 5333 6173 6899 3539 MC8b = 87784
21767 1823 5879 14423 16547 5639 15767 5939 3119 18743 14303 7727 1367 21599 4787 16139 11483 7643 3203 21563 4919 12107 5399 21467 7523 15683 20507 179 21059 4547 17939 347 14699 563 12983 15647 7703 5099 12647 18443 2063 15287 8423 18119 17483 14243 2579 9587 13967 6659 13523 9743 8039 12203 14867 8783 13163 21383 8963 383 10667 12347 13799 7079
Attachment 14.17.12
contains a few more sets of Sophie Germain Simple Magic Squares,
which can be used to construct
pairs of Composed Sophie Germain Magic Squares of order 8
(ref. Priem4c2).
14.17.7 Magic Squares, Composed (9 x 9)
Pairs of Composed Sophie Germain Magic Squares of order 9
can be constructed based on a combination of order 3 Magic Center Squares with 8 Semi Magic Squares (6 Magic Lines).
14.17.8 Magic Squares, Composed (10 x 10)
Pairs of Composed Sophie Germain Magic Squares of order 10
can be constructed based on a combination of order 4 Magic Center Squares with 4 Semi Magic Corner Squares (6 Magic Lines).
14.17.9 Magic Squares, Composed (12 x 12)
Prime Number Magic Squares of order 12  with Magic Sum 3 * s1  can be composed out of 4^{th} order Prime Number Magic Squares with Magic Sum s1.
The obtained results regarding the miscellaneous types of Prime Number Magic Squares as deducted and discussed in previous sections are summarized in following table: 
Order
Main Characteristics
Subroutine
Results
3
Simple Magic
4
Simple Magic, Smaller Magic Sums
Simple Magic, Larger Magic Sums
Simple Magic, Triplets
5
Simple Magic
Associated
Pan Magic
Concentric
Magic, Square Inlay
Magic, Diamond Inlay
6
Symmetric Main Diagonals
Bordered
7
Bordered
Concentric
8
Composed of Simple Magic Sub Squares
Concentric
9
Magic Center Square, Semi Magic Sub Squares
Concentric
10
Magic Center Square, Semi Magic Corner Squares
Concentric
12
Composed of Simple Magic Sub Squares
Following sections will provide miscellaneous construction methods for Two and Four Way, V type Zig Zag Magic Squares.

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