Problems & Puzzles: Puzzles

Puzzle 1123 Tetractys   On Jan 29, 2023, G.L. Honaker, Jr. sent the following nice puzzle, related to a figure named "Tetractys": The 15 primes in the above figure are: 2, 3, 5, 7, 13, 31, 37, 41, 43, 47, 59, 67, 73, 89 & 631 In later emails he added, "First maximum (24 primes) found by a student of mine. Chris Caldwell confirmed and found the other 8, but they are lost." Q. Can you find these supposed 9 distinct maximum lost solutions, each one having 24 distinct primes (disregarding rotations and reflections), reading only over straight lines?

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During the week 18-24 Feb. 2023, all of the following puzzles found the same 9 distinct asked solutions: Giorgos Kalogeropoulos, Michael Branicky, Oscar Volpatti, Paul Cleary, Emmanuel Vantieghem, J-M Rebert, Gennady Gusev, J_ Rebert, Michael Hürt

To save space I will copy just one of these solutions because no difference is really found in between all of them:

"For compactness, I'll use the following two-line format:
first line with arrangement of digits 0-9, four blocks separated by semicolons;
second line with list of resulting primes.
The given example would be represented as follows:
0; 1, 2; 3, 4, 5; 6, 7, 8, 9.
2, 3, 5, 7, 13, 31, 37, 41, 43, 47, 59, 67, 73, 89, 631.

Nine maximal solutions, sorted by sum of resulting primes.

0; 1, 6; 4, 7, 9; 5, 3, 2, 8.
2, 3, 5, 7, 17, 23, 29, 37, 41, 43, 47, 53, 61, 67, 71, 73, 79, 89, 97, 271, 479, 541, 673, 823.

0; 1, 6; 4, 7, 9; 2, 3, 5, 8.
2, 3, 5, 7, 17, 23, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 89, 97, 241, 479, 571, 673, 853.

0; 1, 6; 4, 7, 8; 2, 3, 9, 5.
2, 3, 5, 7, 17, 23, 37, 41, 43, 47, 59, 61, 67, 71, 73, 79, 89, 97, 179, 239, 241, 593, 673, 971.

0; 1, 3; 4, 7, 5; 2, 6, 9, 8.
2, 3, 5, 7, 13, 17, 31, 37, 41, 47, 53, 59, 67, 71, 73, 79, 89, 97, 179, 241, 269, 673, 853, 971.

0; 1, 3; 4, 7, 8; 5, 6, 9, 2.
2, 3, 5, 7, 13, 17, 29, 31, 37, 41, 47, 67, 71, 73, 79, 83, 89, 97, 179, 283, 541, 569, 673, 971.

0; 1, 3; 4, 7, 2; 5, 6, 9, 8.
2, 3, 5, 7, 13, 17, 23, 29, 31, 37, 41, 47, 67, 71, 73, 79, 89, 97, 179, 541, 569, 673, 823, 971.

6; 7, 1; 0, 4, 8; 9, 5, 3, 2.
2, 3, 5, 7, 17, 23, 41, 43, 47, 53, 59, 61, 67, 71, 83, 281, 347, 359, 541, 709, 743, 907, 953, 6709.

6; 7, 1; 0, 4, 2; 9, 5, 3, 8.
2, 3, 5, 7, 17, 23, 41, 43, 47, 53, 59, 61, 67, 71, 83, 347, 359, 541, 709, 743, 821, 907, 953, 6709.

6; 7, 1; 0, 4, 5; 9, 8, 3, 2.
2, 3, 5, 7, 17, 23, 41, 43, 47, 53, 61, 67, 71, 83, 89, 251, 347, 389, 709, 743, 907, 983, 2389, 6709."