World records

History

The constant progress realised in the extraction of high order integer roots enables people to calculate the 13th roots from a 100-digit number very fast. But to double the number of unknown digits multiplies the difficulty by 10. Beginners can calculate a 13th root from a 100-digit number, but the 13th root from a 200-digit number needs several months of training.

Why the 13th root of a 200-digit number is the supreme category

1. The record time for extracting the 13th root of a 100-digit number is 3.625 s by Alexis Lemaire for giving ALL the 8-digit number, and supposed 0.15 s by Jaime Garcia Serrano for giving the beginning of the 8-digit number.
   The time 3.625 s includes :
   reading the question, calculating the 13th root, displaying the 13th root
   
   This means the 13th root of a 100-digit number is an immediate calculation (1 second), and the recordholder will be the one with the fastest time for writing, not with the fastest time for calculating.
   
2. Every left part and right part of the 13th root of a 100-digit number can be memorized: there are only 3 and 4 digits to be memorized
   Therefore the 13th root of a 100-digit number can be only a record of memorization, where as the 13th root of a 200-digit number is a true task of mental calculation
3. the calculation of the 13th root of a 200-digit number cannot be done using calculators, whose accuracy doesn't reach 16 digits for a 13th root:
   The accuracy necessary for the 13th root of a 200-digit number is 16 digits.
   
4. the 13th root of a 200-digit number begins always by 2, where as the 13th root of a 100-digit number begins always by 4
   Somebody who can calculate the 13th root of a 200-digit number will be able to calculate the non-integer 13th root of a 5-digit number, more common than a non-integer 13th root of a 9-digit number.
5. The number of possibilities for the 13th root of a 200-digit number is 3 93 5 44 3961 77 5 93 with symetry/antisymetry, and whose 13th root is 13.26452, there are amazing coincidences which appear directly in the Book of the Revelation.

   Here are some quotes:

   
   Oleg Stepanov:
   "16 digits for me absolutely unbelievable. If you calculate Mentally it on 1 hour, on my opinion you goes to history like best calculator or best mathematician. Probably I can not do it on paper on this time. Also abacus not help me. And 8 digits calculator not help... "
   "This is new World for me. I even have no ideas how get 16 digits on answer...."
   "We interest because if it is really - this is big mathematic invent. For example, do you interesting man what can fly or somebody who can read mind?"
   
   Gert Mittring
   "The 13th. root from a 200-digit number is to difficult for me. In the best case, I have seven missing digits (from sixteen digits)!"
   
   Robert Fountain
   "To extract the 13th root from a 200 digit number within several minutes is a remarkable feat. If Alexis Lemaire can achieve this in the presence of suitably qualified witnesses, then he must be regarded as the greatest 'integer root calculator' in history."
   
   The calculation of the 13th root of a 200-digit number with a record time is the most difficult task of mental calculation which has ever appeared on the Earth.
   One of the main matters is to find the fastest method ...
   Others are to get the best use ...mentally.
   
   The 13th roots from a 200-digit number belong to the interval:
   2 030 917 620 904 736
   -
   2 424 462 017 082 328
   
   The exact number of possibilities is:
   3 935 44 3961 77 593, nearly 13.26452 raised to the 13th power
   
   
   
   
   

   The 13th power of
   
   

   2

   0

   3

   0

   9

   1

   7

   6

   2

   0

   9

   0

   4

   7

   3

   6

   
   is:

   
   

   1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	7	8	5	9
   4	2	6	4	0	8	8	8	1	1	9	9	5	2	0	4	0	1	0	8
   9	0	0	7	6	1	3	4	7	0	6	4	0	2	4	8	7	5	2	2
   9	4	4	6	3	4	2	8	2	4	5	6	0	3	9	1	1	0	5	2
   4	9	1	0	1	5	1	9	1	3	4	8	4	7	4	4	7	3	0	6
   9	0	2	5	1	2	3	8	3	6	5	3	8	5	1	2	9	4	8	4
   7	3	6	9	2	4	4	4	4	0	5	9	2	6	3	2	6	3	2	3
   2	6	0	2	5	2	1	0	6	5	7	6	7	4	4	5	8	5	8	6
   6	7	9	0	3	0	2	8	8	1	3	6	6	1	6	1	8	6	9	5
   6	3	1	8	1	9	6	0	7	9	9	0	9	2	4	7	3	8	5	6

   
   
   
   

   The 13th power of
   
   

   2

   4

   2

   4

   4

   6

   2

   0

   1

   7

   0

   8

   2

   3

   2

   8

   
   is:

   
   
   

   9	9	9	9	9	9	9	9	9	9	9	9	9	9	7	4	3	0	3	1
   9	5	2	0	4	1	0	9	6	9	8	7	0	7	3	6	8	5	8	6
   7	0	1	4	3	8	7	5	2	5	7	9	4	2	1	6	0	2	7	1
   9	8	2	1	4	4	4	4	2	3	0	6	8	6	6	9	9	4	4	3
   8	1	8	1	4	9	4	2	5	7	4	6	6	4	5	3	6	1	3	3
   4	9	1	5	4	0	8	1	5	3	2	2	9	4	5	2	4	1	0	0
   8	2	7	2	1	6	7	8	4	3	7	0	8	4	9	2	1	4	9	8
   4	4	6	4	4	3	9	0	9	8	4	3	6	8	2	8	4	8	6	5
   2	1	1	1	0	3	9	0	3	8	3	6	7	8	3	6	1	4	4	8
   3	0	7	2	2	3	6	0	6	3	7	5	9	8	4	6	6	0	4	8

   
   
   
   

   The rules

   
   
   
   
   
   1. The record is both the fastest and most accurate calculation of the 13th root of a 200-digit number.
      The accuracy is measured by the number of attempts in a group of attempts, for a given event.
      The number of attempts (written #n)for that event is the number of proposed 200-digit numbers needed to break the record. Refusing one 200-digit number is included in the meaning of one attempt.
      
   2. The record is a test of straightforward mental calculation. The calculator should perform the calculation in his/her head without the aid of any other person and without using a calculating machines, computers, etc. nor may the calculator write the 13th root, the 16-digit number result, down.
      
   3. The competitor may choose to write the number from right to left, to left to right, or in any other order.
      
   4. The correction of a digit is not allowed, writing any other digit than a digit of the 16-digit 13th root is forbidden, and doubting digits(badly written) must not lead to a successful attempt.
      
   5. The number whose 13th root is to be calculated should be randomly selected by computer immediately prior to the calculation and should be displayed to the calculator on a computer screen, board, screen or similar. The given number must be the 13th power of a integer number which belongs to the range 2 030 917 620 904 736--2 424 462 017 082 328.
      
   6. The calculator should write down the answer.
      
   7. The timing begins when the number becomes visible to the competitor and ends at the end of writing the answer.
      
   8. The number of days of attempts is limited to 3 days per year
      
   9. However, if there is only one day of attempts in one year, 3 groups of attempts can be done for that day: the 3 days of attempts can be confounded. In this case, there will be 3 events. If there are only 2 days of attempts, one of these days may contain 2 groups of attempts:2 days of attempts may be confounded for that day, so that 3 groups of attempts(and no more) are allowed in one year
      
   10. The attempt should be announced very soon (some months in advance)to 13th_root@yahoogroups.com
       
   11. The exact date (day, hour) and location(adress) of the attempt must be definively announced at least 168 hours before the beginning of the attempt, as well as the name of the two official witnesses
       
   12. After this announcement, any change will unvalidate the day/group of attempts.
       
   13. Any group of attempts unvalidated is counted as a successless group of attempts.
       
   14. The record must break the existing world record both in accuracy and in speed
       
   15. The first record, by default, is 10¹⁰⁰ seconds and 10¹⁰⁰ attempts.
       
   16. The number of attempts must not be more than the number of attempts of the current record, and will likely be lower.
       
   17. Only the first record of the group of attempts will be accepted: this is the one whose number of previous attempts for that group is the lowest
       
   18. The name of the person making the attempt should be given, along with the date and place.
       
   19. There must be two independant witnesses(one should need no help and no advice from the other one)
       
   20. At least one of the official witnesses must be graduated in mathematics, physics or computer sciences(from recognized universities, not fake titles)
       
   21. At least one of the official witnesses must be an usher (official witness in law) or get this statut.
       
   22. The both witnesses must have read and understand the rules at least 168 hours before the attempts, and sent their approval to 13th_root@yahoogroups.com before this deadline.
       
   23. In this approval, they must say, without any lie, they are competent enough for all details of the attempt.
       
   24. Any false sentence written among the witnesses ' evidences will unvalidate the group of attempts, including any mistake.
       
   25. The press coverage doesn't count at all neither in the value of the record, neither as a witness.
       
   26. To prevent cheating, the competitor must accept any unknown checking and constraints set by the official witnesses; these ones must accept the unknown, secret checking and constraints set by info@13throot.com
       
   27. The competitor must also announce in advance the best performance he could get for the group of attempts: the better will be the performance, the higher will be the checking. If the performance is clearly much more amazing than announced, it will be not validated.
       
   28. All the 13th roots from a 200-digit number correctly calculated must be included in the documentation, in an official group of attempts
       
   29. the source code must be kept by the usher(and otherwitnesses) and the program must be compiled by the usher/witnesses, with written details of the process, immediately before the attempt. This rule allows to be sure that the source code of the program used for the record is known.
       
   30. The 2 witnesses MUST keep the sources codes and all the documentation
       
   31. Since many random numbers generators depends on the clock, the clock of the computer must be modified by the witnesses, within a 10 years range after the date of the event. For instance if the record is attempted on the 7/7/7, then the clock of the computer must be modified to belong to the range 8/7/7 - 7/7/17. No favorite date must be preferred in this clock's range.
   
   
   

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