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April 2019 - Solution
One can solve for the same prime average for all rows, columns, and diagonals. For example:
17 89 71 113 59 5 47 29 101
Another general solution that also works for larger squares is to find an arithmetic progression of prime numbers and build a regular magic square.
Lorenz Reichel sent us a solution in which all the secondary diagonals also have prime averages:
73 43 61 31 79 19 37 7 97
Jingran Lin found nine different prime numbers that *every* triplet of them averages to a prime number:[440377009, 1109655619, 1206997621, 1371035311, 1778934229, 2448212839, 3117491449, 3786770059, 4456048669]
Thanks also to Marcelo M De Barros for his blog post on the challenge.