Extracting the 13th root of a number is a famous category for the mental calculationworld records. The challenge consists of being given a large number (possibly over 100 digits) and asked to return the number that equals it when multiplied by itself 13 times. Mental calculation is the practice of doing mathematical calculations using only the human brain, with no help from any computing devices. ... A world record is the best performance in a certain discipline, usually a sports event. ...
Properties of the challenge
Extracting the 13th root has certain properties. One is that the 13th root of a number is much smaller: a 13th root will have approximately 1/13th the number of digits. Thus the 13th root of a 100-digit number only has 8 digits and the 13th root of a 200-digit number will have 16 digits. Further, the last digit of the 13th root is always the same as the last digit of the power. a cow In vascular plants, the root is that organ of a plant body that typically lies below the surface of the soil (compare with stem). ...
For the 13th root of a 100-digit number there are 7992563 possibilities, in the range 41246264 - 49238826. This is considered a relatively easy calculation. The 13th root of a 200-digit number there are 393544396177593 possibilities, in the range 2030917620904736 - 2424462017082328. This is considered a difficult calculation.
Records
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. The Guinness Book of Records (or in recent editions Guinness World Records, and in previous US editions Guinness Book of World Records) is a book published annually, containing an internationally recognized collection of superlatives: both in terms of human achievement and the extrema of the natural world. ...
The first record was 23 minutes by De Grote(Mexico).
The most published time was 88.8 seconds by Klein(Netherlands).
Gert Mittring calculated it in 38 seconds.
Alexis Lemaire has broken his record with the 13.55 seconds. This is the last official world record for extracting the 13th root of a 100-digit number
Alexis Lemaire has also set the first world record for the 13th root of a 200-digit number: 513.55 seconds and 742 attempts on April 6th, 2005, and broken it with 267.77 seconds and 577 attempts on June 3rd, 2005:
ROOT 3rd b5th b7th b9th 11th 13th -------------------------------------------------------------- There it is. Of course there are other chords such as no-5th or no 3rd and such, however if you understand this list, most everything else derived from this list.
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