Program Order5 makes the 275,305,224 order 5 magic squares.
Here are the first and last 5x5 magic squares, (in Frénicle standard form sorted in ascending order):
This is the type summary from program GetType:
Note: Pandiagonal 1-way does not include pandiagonal.
There are 101,774,553 complement pair pattern groups. The squares of 4,845,739 groups have center 13. See all groups, center 13 groups, center not 13 groups.
Order5count counts the squares in 4 minutes on a personal computer at 3.0GHz, (see counting detail):
Manufacturer: Dell Model: Alienware Area-51 R2 Processor: Intel® Core™i7-5960X CPU @ 3.00GHz 3.00GHz Memory(RAM): 32.0 GB System type: 64-bit Operating System Windows edition: Windows 10 Home Environment: Microsoft® Visual C++® 2010 Express Edition
The counts of squares for each cell number by position are: .txt
For example, there are 35,472,326 squares with 1 in a corner cell, another 35,472,326 squares with 1 in a cell one in from a corner along a main diagonal, 4,365,792 squares with 1 in the center cell, and so on.
Since each number from 1 to 25 is somewhere in every square, each row in the table totals 275,305,224. The column totals, (including row 1 to 12 numbers twice), are 275,305,224 multiplied by the number of green cells at the top.