Problems & Puzzles: Puzzles
Puzzle 81.- Sophie Germain primes - magic squares
A very natural extension of the Puzzle 80 is to ask for couples of magic squares such that the corresponding cells contain couples of Sophie Germain primes.
For the magic squares 3x3, here are what I think are the smallest examples, that I have found:
Couple of Magic Squares 3x3, Sophie Germain 1st order
Couple of Magic Squares 3x3, Sophie Germain 2nd order
a) Can you find smaller examples of
these 3x3 Magic Squares?
Felice Russo has found smaller examples of SG 3x3 squares 1st and 2nd order:
1481 1889 2063
2963 3779 4127
3391 3697 7639 6781
He has sent also some ideas for other puzzles with prime-magic squares that soon I'll post in future puzzles pages.
John E. Everett sent (24/03/2000) the following 4x4 prime SG 2nd order type:
(the lower one)