The 13th Root: The Apocalyptical and Official Integer Root

Last month, a French student named Alexis Lemaire became the first human to mentally calculate the 13th root of a 200-digit number:
83689566882369569398
37328662225645224726
78046649383667749735
75581573035075704089
62528802385783156837
68029349382010563433
63855595931514450415
14949070941909770444
93056602684027718696
24155688082648640933
He arrived at the correct 16-digit answer, 2391481494636373, without writing or typing, in 513.55 seconds. Last year he set a new unofficial record for finding the 13th root of a 100-digit number: 3.62 seconds.
All of this is more than sufficiently impressive, but we encourage the curious reader to descend into the depths of 13th root madness by visiting the web site “13th Root: The Apocalyptic and Official Integer Root,” and to explore the 13th root message group and its bizarre gematria / apocalyptic / messianic speculations about the meaning of 13th roots.
How does one mentally calculate the 13th root of a such a large number? The answer can be found in this excerpt from Steven Smith’s book The Great Mental Calculators: The Psychology, Methods, and Lives of Calculating Prodigies Past and Present.
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