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. ==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. ==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 seems to have calculated it in 39 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 : http://www.13throot.com ==External links== *[http://www.13throot.com/ The official 13th root site] Mathematical games
Does 'last' record mean the current record or does it mean the record has been closed and no better records will be listed? User:RJFJR 16:43, Jan 1, 2005 (UTC) The fact that a 13th root has 1/13th the digits of the power can be demonstrated using logarithms. I didn't feel this complexity was necessary to the article but it might be interesting to point people to mathematics and logarithms. User:RJFJR 16:43, Jan 1, 2005 (UTC)
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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. ==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. ==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 seems to have calculated it in 39 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 : http://www.13throot.com ==External links== *[http://www.13throot.com/ The official 13th root site] Mathematical games
13th root
Does 'last' record mean the current record or does it mean the record has been closed and no better records will be listed? User:RJFJR 16:43, Jan 1, 2005 (UTC) The fact that a 13th root has 1/13th the digits of the power can be demonstrated using logarithms. I didn't feel this complexity was necessary to the article but it might be interesting to point people to mathematics and logarithms. User:RJFJR 16:43, Jan 1, 2005 (UTC)
See other meanings of words starting from letter:A | B | C | C | D | E | F | G | H | I | J | K | L | M | N | O | P | R | S | T | U | V | X | Y | Z |
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