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.

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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