1.   A magic square stays magic if its members are each increased by the same amount, or if they are all multiplied by the same amount.
     
2.  The 'smallest' magic square contains the numbers 1 to 9, with a common difference of 1 and  a magic constant of 15.     
      
Starting with e.g. A014092 it seem that there is no run of 9 sums of 2 primes with a common difference of 1 less than 100     
      
With a common difference of 2, and noting that the problem doesn't require distinct primes, we do not need to conjecture that A014091 contains the first 9 even numbers from 4 onwards.     
      
So     
      
5+5 17+3 3+3   
5+3 7+5 13+3   
13+5 2+2 7+7   
      
is the smallest solution, with a magic constant of 36. The basic square is the Lo Shu square, with each number doubled.

Posted by broll on 2013-01-03 00:09:00