which enable the development of a fast procedure to generate Prime Number Concentric Magic Squares of order 14 (ref. Priem14a).
Miscellaneous Prime Number Concentric Magic Squares of order 14, based on 12th order Concentric Magic Squares as discussed in Section 14.32.1, are shown in Attachment 14.34.1.
14.34.2 Magic Squares, Bordered (14 x 14)
Based on the collections of 12th order Composed and miscellaneous Bordered Magic Squares, as discussed in
Section 14.32.2
also following 14th order Bordered Magic Squares can be generated with routine Priem14a:
It should be noted that the Attachments listed above contain only those solutions which could be found within 10 seconds.
Each square shown corresponds with numerous squares for the same Magic Sum.
14.34.3 Magic Squares, Inlaid (14 x 14)
Order 5 Ultra Magic Square Inlays
The 14th order Prime Number Inlaid Magic Square shown below,
is composed out of a Concentric Border,
an Associated Border and four each 5th order Embedded Ultra Magic Squares with different Magic Sums.
Mc14 = 46200
23 |
127 |
6521 |
6529 |
29 |
173 |
6451 |
6547 |
37 |
131 |
457 |
6337 |
6389 |
6449 |
487 |
6581 |
6569 |
6491 |
3019 |
1009 |
907 |
277 |
379 |
2389 |
5861 |
5939 |
179 |
6113 |
6317 |
6329 |
5813 |
2753 |
857 |
4973 |
1019 |
5987 |
2699 |
1181 |
3251 |
2927 |
1811 |
283 |
6373 |
4229 |
683 |
4799 |
1523 |
5153 |
3257 |
941 |
3011 |
3677 |
4967 |
3449 |
3911 |
227 |
233 |
2633 |
863 |
5657 |
3083 |
509 |
5303 |
2657 |
5717 |
3209 |
701 |
3761 |
5507 |
6367 |
389 |
2087 |
2909 |
1013 |
4643 |
1367 |
5483 |
2969 |
1451 |
2741 |
3407 |
5477 |
6053 |
6211 |
6217 |
1871 |
5147 |
1193 |
5309 |
3413 |
353 |
3491 |
3167 |
5237 |
3719 |
431 |
6269 |
383 |
6361 |
331 |
6553 |
1951 |
1789 |
4903 |
1759 |
6277 |
2677 |
2311 |
4567 |
1753 |
4729 |
239 |
241 |
547 |
1669 |
4783 |
3319 |
3673 |
3511 |
1597 |
3853 |
3307 |
4597 |
4231 |
4513 |
6359 |
719 |
1093 |
439 |
5233 |
3391 |
1549 |
6343 |
1627 |
6151 |
3517 |
883 |
5407 |
3967 |
5881 |
6199 |
2689 |
3271 |
3109 |
3463 |
1999 |
5113 |
2803 |
2437 |
3727 |
3181 |
5437 |
2371 |
401 |
6203 |
4789 |
5023 |
1879 |
4993 |
4831 |
229 |
5281 |
2467 |
4723 |
4357 |
757 |
271 |
397 |
6287 |
6421 |
661 |
739 |
4211 |
6221 |
6323 |
5693 |
5591 |
3581 |
109 |
31 |
19 |
313 |
151 |
6473 |
79 |
71 |
6571 |
6427 |
149 |
53 |
6563 |
6469 |
6143 |
263 |
211 |
6577 |
|
s5
|
The method to generate the order 12 Inlaid Magic Center Square with Order 5 Embedded Ultra Magic Squares with different Magic Sums
has been discussed in Section 14.21.4.
The order 14 Bordered Magic Square shown above can be transformed into the Window Type Magic Square shown below:
Mc14 = 46200
23 |
127 |
6521 |
6529 |
29 |
173 |
6451 |
6547 |
37 |
131 |
457 |
6337 |
6389 |
6449 |
487 |
5813 |
2753 |
857 |
4973 |
1019 |
6329 |
1811 |
5987 |
2699 |
1181 |
3251 |
2927 |
6113 |
6317 |
683 |
4799 |
1523 |
5153 |
3257 |
4229 |
3911 |
941 |
3011 |
3677 |
4967 |
3449 |
283 |
6373 |
863 |
5657 |
3083 |
509 |
5303 |
2633 |
5507 |
2657 |
5717 |
3209 |
701 |
3761 |
227 |
233 |
2909 |
1013 |
4643 |
1367 |
5483 |
2087 |
6053 |
2969 |
1451 |
2741 |
3407 |
5477 |
6367 |
389 |
5147 |
1193 |
5309 |
3413 |
353 |
1871 |
6269 |
3491 |
3167 |
5237 |
3719 |
431 |
6211 |
6217 |
6569 |
6491 |
3019 |
1009 |
907 |
6581 |
179 |
277 |
379 |
2389 |
5861 |
5939 |
383 |
6361 |
661 |
739 |
4211 |
6221 |
6323 |
6421 |
19 |
5693 |
5591 |
3581 |
109 |
31 |
239 |
241 |
6553 |
1951 |
1789 |
4903 |
1759 |
331 |
4729 |
6277 |
2677 |
2311 |
4567 |
1753 |
6359 |
719 |
1669 |
4783 |
3319 |
3673 |
3511 |
547 |
4513 |
1597 |
3853 |
3307 |
4597 |
4231 |
5881 |
6199 |
439 |
5233 |
3391 |
1549 |
6343 |
1093 |
3967 |
1627 |
6151 |
3517 |
883 |
5407 |
401 |
6203 |
3271 |
3109 |
3463 |
1999 |
5113 |
2689 |
2371 |
2803 |
2437 |
3727 |
3181 |
5437 |
397 |
6287 |
5023 |
1879 |
4993 |
4831 |
229 |
4789 |
271 |
5281 |
2467 |
4723 |
4357 |
757 |
313 |
151 |
6473 |
79 |
71 |
6571 |
6427 |
149 |
53 |
6563 |
6469 |
6143 |
263 |
211 |
6577 |
|
s5
|
Attachment 14.34.3 page 1, shows for a few Magic Sums the first occurring Bordered Magic Square,
Attachment 14.34.3 page 2, shows the corresponding Window Type Magic Square.
Each square shown corresponds with numerous solutions, which can be obtained by selecting other aspects of the four inlays and variation of the borders (window).
14.34.4 Magic Squares, Eccentric (14 x 14)
Also for Prime Number Eccentric Magic Squares of order 14 it is convenient to split the supplementary rows and columns into:
parts summing to s5 = 5 * s14 / 14 and s4 = 4 * s14 / 14:
a1 |
a2 |
a3 |
a4 |
a5 |
a6 |
a7 |
a8 |
a9 |
a10 |
a11 |
a12 |
a13 |
a14 |
a15 |
a16 |
a17 |
a18 |
a19 |
a20 |
a21 |
a22 |
a23 |
a24 |
a25 |
a26 |
a27 |
a28 |
a29 |
a30 |
a31 |
a32 |
a33 |
a34 |
a35 |
a36 |
a37 |
a38 |
a39 |
a40 |
a41 |
a42 |
a43 |
a44 |
a45 |
a46 |
a47 |
a48 |
a49 |
a50 |
a51 |
a52 |
a53 |
a54 |
a55 |
a56 |
a57 |
a58 |
a59 |
a60 |
a61 |
a62 |
a63 |
a64 |
a65 |
a66 |
a67 |
a68 |
a69 |
a70 |
a71 |
a72 |
a73 |
a74 |
a75 |
a76 |
a77 |
a78 |
a79 |
a80 |
a81 |
a82 |
a83 |
a84 |
a85 |
a86 |
a87 |
a88 |
a89 |
a90 |
a91 |
a92 |
a93 |
a94 |
a95 |
a96 |
a97 |
a98 |
a99 |
a100 |
a101 |
a102 |
a103 |
a104 |
a105 |
a106 |
a107 |
a108 |
a109 |
a110 |
a111 |
a112 |
a113 |
a114 |
a115 |
a116 |
a117 |
a118 |
a119 |
a120 |
a121 |
a122 |
a123 |
a124 |
a125 |
a126 |
a127 |
a128 |
a129 |
a130 |
a131 |
a132 |
a133 |
a134 |
a135 |
a136 |
a137 |
a138 |
a139 |
a140 |
a141 |
a142 |
a143 |
a144 |
a145 |
a146 |
a147 |
a148 |
a149 |
a150 |
a151 |
a152 |
a153 |
a154 |
a155 |
a156 |
a157 |
a158 |
a159 |
a160 |
a161 |
a162 |
a163 |
a164 |
a165 |
a166 |
a167 |
a168 |
a169 |
a170 |
a171 |
a172 |
a173 |
a174 |
a175 |
a176 |
a177 |
a178 |
a179 |
a180 |
a181 |
a182 |
a183 |
a184 |
a185 |
a186 |
a187 |
a188 |
a189 |
a190 |
a191 |
a192 |
a193 |
a194 |
a195 |
a196 |
This enables, based on the same principles, the development of a fast procedure (ref. Priem14b):
-
to read the previously generated Eccentric Magic Squares of order 12;
-
to complete the Main Diagonal and determine the related Border Pairs;
-
to generate, based on the remainder of the available pairs, a suitable Corner Square of order 4;
-
to complete the Eccentric Magic Square of order 14 with the two remaining 2 x 5 Magic Rectangles.
Attachment 14.34.2 shows,
based on the 12th order Eccentric Magic Squares as discussed in Section 14.32.5,
one Prime Number Eccentric Magic Square for some of the occurring Magic Sums.
Each square shown corresponds with numerous squares for the same Magic Sum.
14.34.5 Magic Squares, Composed (14 x 14)
Center Cross
The 14th order Prime Number Composed Magic Square shown below:
Mc14 = 24990
3049 |
2269 |
37 |
1987 |
2797 |
571 |
433 |
3137 |
2017 |
3067 |
271 |
2801 |
2357 |
197 |
2293 |
1303 |
1759 |
3259 |
859 |
1237 |
3307 |
263 |
3181 |
631 |
1543 |
2447 |
1289 |
1619 |
13 |
1783 |
3559 |
109 |
1699 |
3547 |
3329 |
241 |
157 |
1657 |
3541 |
107 |
1709 |
3539 |
1583 |
773 |
2999 |
521 |
1301 |
3533 |
227 |
3343 |
769 |
1213 |
3373 |
1553 |
503 |
3299 |
311 |
2711 |
2333 |
1277 |
2267 |
1811 |
239 |
3331 |
1123 |
2281 |
1951 |
389 |
2939 |
2027 |
3461 |
1871 |
23 |
3557 |
1787 |
11 |
2311 |
1259 |
3463 |
1861 |
31 |
3413 |
1913 |
29 |
179 |
3433 |
3457 |
79 |
101 |
2039 |
71 |
3313 |
3347 |
3359 |
163 |
199 |
2081 |
3169 |
3391 |
137 |
113 |
3491 |
3469 |
1531 |
257 |
3499 |
223 |
211 |
3407 |
3371 |
1489 |
401 |
3253 |
1429 |
673 |
2003 |
2843 |
509 |
2927 |
643 |
3319 |
1327 |
709 |
2287 |
2521 |
547 |
1999 |
2203 |
1153 |
3083 |
953 |
1319 |
3221 |
349 |
1669 |
2557 |
1129 |
2887 |
1171 |
1297 |
103 |
1723 |
3529 |
269 |
1559 |
3527 |
313 |
3257 |
367 |
1471 |
3517 |
181 |
1663 |
3511 |
1567 |
727 |
3061 |
317 |
2141 |
2897 |
2089 |
1481 |
1283 |
1049 |
3023 |
251 |
2243 |
2861 |
487 |
2617 |
2251 |
1571 |
1367 |
2417 |
3079 |
491 |
683 |
2399 |
2273 |
1901 |
1013 |
2441 |
3301 |
2011 |
43 |
3467 |
1847 |
41 |
3187 |
383 |
3389 |
1907 |
59 |
3203 |
2099 |
53 |
is an example of a Prime Number Magic Square with Magic Sum s14, composed of:
-
Four each 6th order (Pan) Magic Corner Squares (s6 = 6 * s14 / 14),
-
Twentysix supplementary pairs, each summing to 2 * s14 / 14
Subject Composed Magic Squares can be obtained by transformation of Bordered Magic Squares with Composed Magic Center Squares
as discussed in Section 14.34.2 above.
Attachment 14.34.36 shows for a few Magic Sums the first occurring 14th order Prime Number Composed Magic Square.
14.34.6 Magic Squares, Inlaid (14 x 14)
The 14th order Prime Number Inlaid Magic Square shown below:
Mc14 = 24990
3319 |
1327 |
709 |
433 |
3253 |
1429 |
673 |
2003 |
2843 |
509 |
3137 |
2287 |
2521 |
547 |
1669 |
2557 |
1129 |
3307 |
1999 |
2203 |
1153 |
3083 |
953 |
1319 |
263 |
2887 |
1171 |
1297 |
367 |
1471 |
3517 |
3329 |
103 |
1723 |
3529 |
269 |
1559 |
3527 |
241 |
181 |
1663 |
3511 |
179 |
3433 |
3457 |
71 |
79 |
101 |
2039 |
3347 |
3359 |
163 |
3313 |
199 |
2081 |
3169 |
2017 |
3067 |
271 |
227 |
3049 |
2269 |
37 |
1987 |
2797 |
571 |
3343 |
2801 |
2357 |
197 |
3181 |
631 |
1543 |
239 |
2293 |
1303 |
1759 |
3259 |
859 |
1237 |
3331 |
2447 |
1289 |
1619 |
157 |
1657 |
3541 |
2311 |
13 |
1783 |
3559 |
109 |
1699 |
3547 |
1259 |
107 |
1709 |
3539 |
769 |
1213 |
3373 |
2927 |
1583 |
773 |
2999 |
521 |
1301 |
3533 |
643 |
1553 |
503 |
3299 |
1123 |
2281 |
1951 |
3221 |
311 |
2711 |
2333 |
1277 |
2267 |
1811 |
349 |
389 |
2939 |
2027 |
3463 |
1861 |
31 |
313 |
3461 |
1871 |
23 |
3557 |
1787 |
11 |
3257 |
3413 |
1913 |
29 |
3391 |
137 |
113 |
257 |
3491 |
3469 |
1531 |
223 |
211 |
3407 |
3499 |
3371 |
1489 |
401 |
1283 |
1049 |
3023 |
2089 |
1567 |
727 |
3061 |
317 |
2141 |
2897 |
1481 |
251 |
2243 |
2861 |
683 |
2399 |
2273 |
3079 |
487 |
2617 |
2251 |
1571 |
1367 |
2417 |
491 |
1901 |
1013 |
2441 |
3389 |
1907 |
59 |
3187 |
3301 |
2011 |
43 |
3467 |
1847 |
41 |
383 |
3203 |
2099 |
53 |
is an example of a Prime Number Inlaid Magic Square with Magic Sum s14, composed of:
-
Three each 6th order (Pan) Magic Square Inlays (s6 = 6 * s14 / 14),
-
One 6th order (Pan) Magic Center Square (s6 = 6 * s14 / 14),
-
Twentysix supplementary pairs, each summing to 2 * s14 / 14
Subject Inlaid Magic Squares can be obtained by transformation of Composed Magic Squares
as discussed in Section 14.32.4 above.
Attachment 14.34.37 shows for a few Magic Sums the first occurring 14th order Prime Number Inlaid Magic Square.
14.34.7 Associated Magic Squares (14 x 14)
Composed of Semi Magic Squares (7 x 7)
Associated Magic Squares, composed of four each Semi Magic Squares, contain two sets of Complementary Anti Symmetric Semi Magic Squares,
which can be arranged as illustrated below:
Mc14 = 85414
719 |
683 |
10883 |
12119 |
11939 |
5711 |
653 |
3911 |
4919 |
9473 |
11633 |
7829 |
3449 |
1493 |
131 |
941 |
11321 |
12011 |
11813 |
2789 |
3701 |
4253 |
5099 |
8951 |
10331 |
10253 |
2711 |
1109 |
11393 |
10631 |
2111 |
269 |
419 |
8423 |
9461 |
5939 |
8273 |
4091 |
2039 |
4409 |
7853 |
10103 |
12161 |
12149 |
89 |
5 |
233 |
7481 |
10589 |
10301 |
6113 |
1889 |
401 |
1913 |
10391 |
11699 |
3191 |
1229 |
9851 |
10133 |
3659 |
3371 |
11273 |
8669 |
6173 |
3461 |
9803 |
5081 |
5981 |
3539 |
3203 |
5903 |
7229 |
8069 |
2963 |
8369 |
6971 |
8123 |
4679 |
5501 |
6899 |
10223 |
2579 |
4703 |
11909 |
11171 |
1223 |
101 |
11681 |
6563 |
59 |
1511 |
7451 |
9341 |
1601 |
2999 |
9743 |
10061 |
2141 |
2459 |
9203 |
10601 |
2861 |
4751 |
10691 |
12143 |
5639 |
521 |
12101 |
10979 |
1031 |
293 |
7499 |
9623 |
1979 |
5303 |
6701 |
7523 |
4079 |
5231 |
3833 |
9239 |
4133 |
4973 |
6299 |
8999 |
8663 |
6221 |
7121 |
2399 |
8741 |
6029 |
3533 |
929 |
8831 |
8543 |
2069 |
2351 |
10973 |
9011 |
503 |
1811 |
10289 |
11801 |
10313 |
6089 |
1901 |
1613 |
4721 |
11969 |
12197 |
12113 |
53 |
41 |
2099 |
4349 |
7793 |
10163 |
8111 |
3929 |
6263 |
2741 |
3779 |
11783 |
11933 |
10091 |
1571 |
809 |
11093 |
9491 |
1949 |
1871 |
3251 |
7103 |
7949 |
8501 |
9413 |
389 |
191 |
881 |
11261 |
12071 |
10709 |
8753 |
4373 |
569 |
2729 |
7283 |
8291 |
11549 |
6491 |
263 |
83 |
1319 |
11519 |
11483 |
Due to the chosen arrangement the Composed Associated Magic Square shown above contains an order 6 Associated Magic Centre Square and an order 8 Associated Square Inlay.
-
Attachment 14.34.41 shows of few more examples of suitable 7th order Anti Symmetric Semi Magic Squares,
containing order 3 and 4 Semi Magic Sub Squares (ref. PriemSqrs7).
-
Attachment 14.34.42 shows for miscellaneous Magic Sums the related 14th order Associated Magic Squares;
-
Attachment 14.34.43 shows the corresponding Pan Magic and Complete Magic Squares (Eulers Transformation).
Subject Composed Magic Squares can be transformed into (Inlaid) Four Way V type ZigZag Magic Squares by means of the transformation illustrated below for respectively:
Inlaid Four Way V type ZigZag Associated Magic Square B1, Mc14 = 85414:
A1 (Associated)
719 |
683 |
10883 |
12119 |
11939 |
5711 |
653 |
3911 |
4919 |
9473 |
11633 |
7829 |
3449 |
1493 |
131 |
941 |
11321 |
12011 |
11813 |
2789 |
3701 |
4253 |
5099 |
8951 |
10331 |
10253 |
2711 |
1109 |
11393 |
10631 |
2111 |
269 |
419 |
8423 |
9461 |
5939 |
8273 |
4091 |
2039 |
4409 |
7853 |
10103 |
12161 |
12149 |
89 |
5 |
233 |
7481 |
10589 |
10301 |
6113 |
1889 |
401 |
1913 |
10391 |
11699 |
3191 |
1229 |
9851 |
10133 |
3659 |
3371 |
11273 |
8669 |
6173 |
3461 |
9803 |
5081 |
5981 |
3539 |
3203 |
5903 |
7229 |
8069 |
2963 |
8369 |
6971 |
8123 |
4679 |
5501 |
6899 |
10223 |
2579 |
4703 |
11909 |
11171 |
1223 |
101 |
11681 |
6563 |
59 |
1511 |
7451 |
9341 |
1601 |
2999 |
9743 |
10061 |
2141 |
2459 |
9203 |
10601 |
2861 |
4751 |
10691 |
12143 |
5639 |
521 |
12101 |
10979 |
1031 |
293 |
7499 |
9623 |
1979 |
5303 |
6701 |
7523 |
4079 |
5231 |
3833 |
9239 |
4133 |
4973 |
6299 |
8999 |
8663 |
6221 |
7121 |
2399 |
8741 |
6029 |
3533 |
929 |
8831 |
8543 |
2069 |
2351 |
10973 |
9011 |
503 |
1811 |
10289 |
11801 |
10313 |
6089 |
1901 |
1613 |
4721 |
11969 |
12197 |
12113 |
53 |
41 |
2099 |
4349 |
7793 |
10163 |
8111 |
3929 |
6263 |
2741 |
3779 |
11783 |
11933 |
10091 |
1571 |
809 |
11093 |
9491 |
1949 |
1871 |
3251 |
7103 |
7949 |
8501 |
9413 |
389 |
191 |
881 |
11261 |
12071 |
10709 |
8753 |
4373 |
569 |
2729 |
7283 |
8291 |
11549 |
6491 |
263 |
83 |
1319 |
11519 |
11483 |
B1 (Associated)
719 |
3911 |
683 |
4919 |
10883 |
9473 |
12119 |
11633 |
11939 |
7829 |
5711 |
3449 |
653 |
1493 |
2141 |
12143 |
2459 |
5639 |
9203 |
521 |
10601 |
12101 |
2861 |
10979 |
4751 |
1031 |
10691 |
293 |
131 |
4253 |
941 |
5099 |
11321 |
8951 |
12011 |
10331 |
11813 |
10253 |
2789 |
2711 |
3701 |
1109 |
7499 |
5231 |
9623 |
3833 |
1979 |
9239 |
5303 |
4133 |
6701 |
4973 |
7523 |
6299 |
4079 |
8999 |
11393 |
5939 |
10631 |
8273 |
2111 |
4091 |
269 |
2039 |
419 |
4409 |
8423 |
7853 |
9461 |
10103 |
8663 |
929 |
6221 |
8831 |
7121 |
8543 |
2399 |
2069 |
8741 |
2351 |
6029 |
10973 |
3533 |
9011 |
12161 |
10301 |
12149 |
6113 |
89 |
1889 |
5 |
401 |
233 |
1913 |
7481 |
10391 |
10589 |
11699 |
503 |
1613 |
1811 |
4721 |
10289 |
11969 |
11801 |
12197 |
10313 |
12113 |
6089 |
53 |
1901 |
41 |
3191 |
8669 |
1229 |
6173 |
9851 |
3461 |
10133 |
9803 |
3659 |
5081 |
3371 |
5981 |
11273 |
3539 |
2099 |
2741 |
4349 |
3779 |
7793 |
11783 |
10163 |
11933 |
8111 |
10091 |
3929 |
1571 |
6263 |
809 |
3203 |
8123 |
5903 |
4679 |
7229 |
5501 |
8069 |
6899 |
2963 |
10223 |
8369 |
2579 |
6971 |
4703 |
11093 |
8501 |
9491 |
9413 |
1949 |
389 |
1871 |
191 |
3251 |
881 |
7103 |
11261 |
7949 |
12071 |
11909 |
1511 |
11171 |
7451 |
1223 |
9341 |
101 |
1601 |
11681 |
2999 |
6563 |
9743 |
59 |
10061 |
10709 |
11549 |
8753 |
6491 |
4373 |
263 |
569 |
83 |
2729 |
1319 |
7283 |
11519 |
8291 |
11483 |
Inlaid Four Way V type ZigZag Croswise Symmetric Magic Square B2, Mc14 = 85414:
A2 (Complete)
719 |
683 |
10883 |
12119 |
11939 |
5711 |
653 |
1493 |
3449 |
7829 |
11633 |
9473 |
4919 |
3911 |
131 |
941 |
11321 |
12011 |
11813 |
2789 |
3701 |
1109 |
2711 |
10253 |
10331 |
8951 |
5099 |
4253 |
11393 |
10631 |
2111 |
269 |
419 |
8423 |
9461 |
10103 |
7853 |
4409 |
2039 |
4091 |
8273 |
5939 |
12161 |
12149 |
89 |
5 |
233 |
7481 |
10589 |
11699 |
10391 |
1913 |
401 |
1889 |
6113 |
10301 |
3191 |
1229 |
9851 |
10133 |
3659 |
3371 |
11273 |
3539 |
5981 |
5081 |
9803 |
3461 |
6173 |
8669 |
3203 |
5903 |
7229 |
8069 |
2963 |
8369 |
6971 |
4703 |
2579 |
10223 |
6899 |
5501 |
4679 |
8123 |
11909 |
11171 |
1223 |
101 |
11681 |
6563 |
59 |
10061 |
9743 |
2999 |
1601 |
9341 |
7451 |
1511 |
10709 |
8753 |
4373 |
569 |
2729 |
7283 |
8291 |
11483 |
11519 |
1319 |
83 |
263 |
6491 |
11549 |
11093 |
9491 |
1949 |
1871 |
3251 |
7103 |
7949 |
12071 |
11261 |
881 |
191 |
389 |
9413 |
8501 |
2099 |
4349 |
7793 |
10163 |
8111 |
3929 |
6263 |
809 |
1571 |
10091 |
11933 |
11783 |
3779 |
2741 |
503 |
1811 |
10289 |
11801 |
10313 |
6089 |
1901 |
41 |
53 |
12113 |
12197 |
11969 |
4721 |
1613 |
8663 |
6221 |
7121 |
2399 |
8741 |
6029 |
3533 |
9011 |
10973 |
2351 |
2069 |
8543 |
8831 |
929 |
7499 |
9623 |
1979 |
5303 |
6701 |
7523 |
4079 |
8999 |
6299 |
4973 |
4133 |
9239 |
3833 |
5231 |
2141 |
2459 |
9203 |
10601 |
2861 |
4751 |
10691 |
293 |
1031 |
10979 |
12101 |
521 |
5639 |
12143 |
B2 (Crosswise Symmetric)
719 |
1493 |
683 |
3449 |
10883 |
7829 |
12119 |
11633 |
11939 |
9473 |
5711 |
4919 |
653 |
3911 |
10709 |
11483 |
8753 |
11519 |
4373 |
1319 |
569 |
83 |
2729 |
263 |
7283 |
6491 |
8291 |
11549 |
131 |
1109 |
941 |
2711 |
11321 |
10253 |
12011 |
10331 |
11813 |
8951 |
2789 |
5099 |
3701 |
4253 |
11093 |
12071 |
9491 |
11261 |
1949 |
881 |
1871 |
191 |
3251 |
389 |
7103 |
9413 |
7949 |
8501 |
11393 |
10103 |
10631 |
7853 |
2111 |
4409 |
269 |
2039 |
419 |
4091 |
8423 |
8273 |
9461 |
5939 |
2099 |
809 |
4349 |
1571 |
7793 |
10091 |
10163 |
11933 |
8111 |
11783 |
3929 |
3779 |
6263 |
2741 |
12161 |
11699 |
12149 |
10391 |
89 |
1913 |
5 |
401 |
233 |
1889 |
7481 |
6113 |
10589 |
10301 |
503 |
41 |
1811 |
53 |
10289 |
12113 |
11801 |
12197 |
10313 |
11969 |
6089 |
4721 |
1901 |
1613 |
3191 |
3539 |
1229 |
5981 |
9851 |
5081 |
10133 |
9803 |
3659 |
3461 |
3371 |
6173 |
11273 |
8669 |
8663 |
9011 |
6221 |
10973 |
7121 |
2351 |
2399 |
2069 |
8741 |
8543 |
6029 |
8831 |
3533 |
929 |
3203 |
4703 |
5903 |
2579 |
7229 |
10223 |
8069 |
6899 |
2963 |
5501 |
8369 |
4679 |
6971 |
8123 |
7499 |
8999 |
9623 |
6299 |
1979 |
4973 |
5303 |
4133 |
6701 |
9239 |
7523 |
3833 |
4079 |
5231 |
11909 |
10061 |
11171 |
9743 |
1223 |
2999 |
101 |
1601 |
11681 |
9341 |
6563 |
7451 |
59 |
1511 |
2141 |
293 |
2459 |
1031 |
9203 |
10979 |
10601 |
12101 |
2861 |
521 |
4751 |
5639 |
10691 |
12143 |
Each square shown above and in the referred attachments corresponds with numerous squares for the same Magic Sum.
Notes:
For the Associated Magic Squares B1 also the Semi Diagonals sum to the Magic Sum.
For the Crosswise Symmetric Magic Squares B2 also half of the Broken Diagonals sum to the Magic Sum.
14.34.8 Magic Squares, Composed (14 x 14)
The Composed Associated Magic Square shown in Section 14.34.6 above.
can be transformed - by means of row and column permutations -
to the Composed Associated Magic Square shown below:
Mc14 = 85414
3659 |
3371 |
11273 |
3191 |
1229 |
9851 |
10133 |
9803 |
5081 |
5981 |
3539 |
8669 |
6173 |
3461 |
2963 |
8369 |
6971 |
3203 |
5903 |
7229 |
8069 |
6899 |
10223 |
2579 |
4703 |
8123 |
4679 |
5501 |
11681 |
6563 |
59 |
11909 |
11171 |
1223 |
101 |
1601 |
2999 |
9743 |
10061 |
1511 |
7451 |
9341 |
11939 |
5711 |
653 |
719 |
683 |
10883 |
12119 |
11633 |
7829 |
3449 |
1493 |
3911 |
4919 |
9473 |
11813 |
2789 |
3701 |
131 |
941 |
11321 |
12011 |
10331 |
10253 |
2711 |
1109 |
4253 |
5099 |
8951 |
419 |
8423 |
9461 |
11393 |
10631 |
2111 |
269 |
2039 |
4409 |
7853 |
10103 |
5939 |
8273 |
4091 |
233 |
7481 |
10589 |
12161 |
12149 |
89 |
5 |
401 |
1913 |
10391 |
11699 |
10301 |
6113 |
1889 |
10313 |
6089 |
1901 |
503 |
1811 |
10289 |
11801 |
12197 |
12113 |
53 |
41 |
1613 |
4721 |
11969 |
8111 |
3929 |
6263 |
2099 |
4349 |
7793 |
10163 |
11933 |
10091 |
1571 |
809 |
2741 |
3779 |
11783 |
3251 |
7103 |
7949 |
11093 |
9491 |
1949 |
1871 |
191 |
881 |
11261 |
12071 |
8501 |
9413 |
389 |
2729 |
7283 |
8291 |
10709 |
8753 |
4373 |
569 |
83 |
1319 |
11519 |
11483 |
11549 |
6491 |
263 |
2861 |
4751 |
10691 |
2141 |
2459 |
9203 |
10601 |
12101 |
10979 |
1031 |
293 |
12143 |
5639 |
521 |
6701 |
7523 |
4079 |
7499 |
9623 |
1979 |
5303 |
4133 |
4973 |
6299 |
8999 |
5231 |
3833 |
9239 |
8741 |
6029 |
3533 |
8663 |
6221 |
7121 |
2399 |
2069 |
2351 |
10973 |
9011 |
929 |
8831 |
8543 |
The Composed Associated Magic Square shown above contains an order 8 Associated Magic Centre Square and an order 6 Associated Square Inlay.
Attachment 14.34.38 shows for a few Magic Sums the first occurring 14th order
Prime Number Composed Magic Square.
14.34.9 Magic Squares, Order 7 Magic Cube Based
Composed (14 x 14)
Order 14 Prime Number Magic Squares composed of Order 7 (Semi-) Magic Sub Squares can be constructed based on Prime Number Concentric Magic Cubes, as deducted in
Section 7.5 of Chapter 'Prime Number Magic Cubes'.
A typical examples of an order 14 Prime Number Composed Magic Square (Mc14 = 151186), based on planes of a Prime Number Magic Cube of half the Magic Sum, is shown below.
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