Another Amazing 13 x 13 Magic Square

1153	8923	1093	9127	1327	9277	1063	9133	9661	1693	991	8887	8353
9967	8161	3253	2857	6823	2143	4447	8821	8713	8717	3001	3271	907
1831	8167	4093	7561	3631	3457	7573	3907	7411	3967	7333	2707	9043
9907	7687	7237	6367	4597	4723	6577	4513	4831	6451	3637	3187	967
1723	7753	2347	4603	5527	4993	5641	6073	4951	6271	8527	3121	9151
9421	2293	6763	4663	4657	9007	1861	5443	6217	6211	4111	8581	1453
2011	2683	6871	6547	5227	1873	5437	9001	5647	4327	4003	8191	8863
9403	8761	3877	4783	5851	5431	9013	1867	5023	6091	6997	2113	1471
1531	2137	7177	6673	5923	5881	5233	4801	5347	4201	3697	8737	9343
9643	2251	7027	4423	6277	6151	4297	6361	6043	4507	3847	8623	1231
1783	2311	3541	3313	7243	7417	3301	6967	3463	6907	6781	8563	9091
9787	7603	7621	8017	4051	8731	6427	2053	2161	2557	7873	2713	1087
2521	1951	9781	1747	9547	1597	9811	1741	1213	9181	9883	1987	9721

The Journal of Recreational Mathematics published this remarkable magic square, composed by “a puzzlist who at the time was a prison inmate.”  The magic constant is 70,681.

First, it was a pretty good job that he was able to create this by hand (no computers involved).

Second, the magic square contains only prime numbers (which is a difficult constraint to deal with).

Third, the large 13 x 13 square is magic — that is, each row and column adds to the same sum — but so is each successive nested square, from 11 x 11 down to 3 x 3.  That makes 11 magic squares in one!

And fourth, the magic constant of each square is 10,874 smaller than the last.

REFERENCES:

http://www.futilitycloset.com/2010/08/14/time-well-spent/

David