A magic square that remains magic when its border is removed. A nested magic square remains magic after the border is successively removed one ring at a time. An example of a nested magic square is the order 7 square illustrated above (i.e., the order 7, 5, and 3 squares obtained from it are all magic).
The amazing square above (Madachy 1979, pp. 93-94) is a 
prime magic
border square, so that the 
, 
, ..., and 
subsquares are all also prime
magic squares.
