Magic squares of 7th powers
See also the Magic squares of cubes general page

Magic squares of 7th powers have been known since 2004-2005, using very big 65536 x 65536 heptamagic squares, directly raising their integers to the seventh power.

But is it possible to construct smaller squares of 7th powers? Hopefully, yes! In 2012 and 2013, using methods similar to those already used for squares of 6th powers, Jaroslaw Wroblewski and Toshihiro Shirakawa constructed these squares:

 Square Order Date Author S7 MaxNb Semi-magic 196 March 2012 Jaroslaw Wroblewski 3.54e+375 (3.81e+53)^7 81 April 2013 Toshihiro Shirakawa 1.97e+250 (5.59e+35)^7 64 May 2013 3.03e+221 (4.20e+31)^7 Magic 144 September 2013 3.14e+51 18421557^7

The best known = the smallest known magic and semi-magic are these two squares below from Toshihiro Shirakawa.
In his 144x144 magic square, amazing and fun: the 52 digits of S7 are exactly the 52 first digits of the famous number Pi... YES,  !!!!
But not a coincidence... S7 = T1xT2... and in his construction method, he chose T1 and T2 for that.

 477 18574207 34679337 36262447 ... 260857 5107 36747787 39491137 ... 632157 2830507 10097 41846587 ... 670227 6859507 5599957 11497 ... ... ... ... ... ...
 366770087315531181981431366634007 284458648578052236850285053330007 229987843531191170219379404820007 156149641134335057675262859062007 ... 361295906907836686727977167132007 280212997106738024359982291340007 226555189150128615439985682360007 153819049475613638903990279076007 ... 333925004869364210460706169622007 258984739750166961908468481390007 209391917244815841543017070060007 142166091182006545047627379146007 ... 303817012627044486566708072361007 235633656657938793211803290445007 190512318148971790256351596530007 129347837059038741805628189223007 ... ... ... ... ... ...

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