Problems & Puzzles: Puzzles

Puzzle 695 Pandiagonal & twin primes In the puzzle 689 Natalia Makarova sent an object a kind of related to the original question posed by Radko Nachev. She sent a single 4x4 minimal pandiagonal magic square composed of 8 pairs of twin primes and a magical sum of 420. 17 191 31 181 151 61 137 71 179 29 193 19 73 139 59 149 where the twin primes pairs are: (17,19), (29,31), (59,61), (71,73), (137,139), (149,151), (179,181), (191,193) Q. Sent your solutions of this type for the next orders: 5x5, 6x6,... and so on, if the minimal the better.

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On October 27, 2020 Jos Luyendijk wrote:

It is an 8 x 8 Pan Magic Square composed of 32 Twin Pairs and has following  properties:

 

1. The square is Pan Magic, Complete and 4 x 4 Compact;

2. The square contains four 4 x 4 Pan Magic Square Inlays;    

3. The corner points of all 3 x 3 sub squares (64 ea) sum to half the Magic Sum;

4. The corner points of all 5 x 5 sub squares (24 ea) sum to half the Magic Sum;

 

The twin prime pairs are:

 

(11, 13),     (29, 31),     (41, 43),     (101, 103),

(107, 109),   (179, 181),   (197, 199),   (239, 241),

(269, 271),   (311, 313),   (857, 859),   (1019, 1021),

(1229, 1231), (1301, 1303), (1427, 1429), (1487, 1489),

(2081, 2083), (2141, 2143), (2267, 2269), (2339, 2341),

(2549, 2551), (2711, 2713), (3257, 3259), (3299, 3301),

(3329, 3331), (3371, 3373), (3389, 3391), (3461, 3463),

(3467, 3469), (3527, 3529), (3539, 3541), (3557, 3559),

 

Mc8 = 14280
199	1489	3373	2083		179	1427	3389		2141
1021	1303	2551	2269		857	1229	2711		2339
11	41	3557	3527		31	103	3541		3469
107	239	3461	3329		271	313	3301		3259
3391	2143	181	1429		3371	2081	197		1487
2713	2341	859	1231		2549	2267	1019		1301
3539	3467	29	101		3559	3529	13		43
3299	3257	269	311		3463	3331	109		241

 

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