Problems & Puzzles: Puzzles

 Puzzle 723. Pandiagonal magic squares of consecutive primes Natalia Makarova sent the following puzzle. Here are the already known solutions for Pandiagonal magic squares of consecutive primes: n=4 (author Jaroslaw Wroblewski. It is unknown whether this result is minimal.)   320572022166380833 320572022166380921 320572022166380849 320572022166380917320572022166380909 320572022166380857 320572022166380893 320572022166380861 320572022166380911 320572022166380843 320572022166380927 320572022166380839320572022166380867 320572022166380899 320572022166380851 320572022166380903   S=1282288088665523520***   n=6 (minimal solution)   67 193 71 251 109 239  139 233 113 181 157 107  241 97 191 89 163 149  73 167 131 229 151 179  199 103 227 101 127 173  211 137 197 79 223 83   S=930 Q1. For n=4 can you find a smaller solution? Q2. Can you find solutions for n=5 and 7, minimal or not?

On July 30, 2014, Max Alekseyev wrote:

I've just found a minimal pandiagonal 4x4 magic square composed of consecutive primes:

170693941183817 170693941183933 170693941183949 170693941183981
170693941183979 170693941183951 170693941183847 170693941183903
170693941183891 170693941183859 170693941184023 170693941183907
170693941183993 170693941183937 170693941183861 170693941183889

Magic constant (682775764735680).

These primes now form the sequence https://oeis.org/A245721 in the OEIS.

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