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 320572022166380917

320572022166380909 320572022166380857 320572022166380893 320572022166380861

320572022166380911 320572022166380843 320572022166380927 320572022166380839

320572022166380867 320572022166380899 320572022166380851 320572022166380903

S=1282288088665523520
***

n=6 (minimal solution)

http://oeis.org/A073523

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?