Extracting the 13th root of a number is a famous category for the mental calculation world records.
For the 13th root of a 100-digit number there are 7,992,563 possibilities, in the range 41,246,264 – 49,238,826.
There are 393,544,396,177,593 possibilities, in the range 2,030,917,620,904,736 – 2,424,462,017,082,328, for the 13th root of a 200-digit number.
The Guinness Book of World Records has published records for extracting the 13th root of a 100-digit number.
All world records for mentally extracting a 13th root have been for numbers with an integer root: