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13th root

Extracting the 13th root of a number is a famous category for the mental calculation world 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.

13th root - 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.

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.

13th root - 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 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.
• Gert Mittring broke this record unofficially with 11,8 seconds, documented by Prof. Dr. Beuteolspacher, Mathematikum Giessen.
• Alexis Lemaire broke this record unofficially 6 times, twice within 4 seconds the best was 3.625 seconds, at the presidency of the University of Reims

• 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:
• the same day, Alexis Lemaire has also set in front of official witnesses an unofficial record of 113 seconds and 40 attempts

Adapted from the Wikipedia article "13th root", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki