EXTREMELY IMPORTANT INFORMATION: the 13th root of a 200 digit number is currently under investigation for critical research purposes that are also external of the area of mental calculation; if you plan in the future to do anything with the 13th root PLEASE send an email to

and require an answer. Uncontrolled facts related to the 13th root of a 200 digit number could have potentially critical AND EXTREMELY GRAVE AND SERIOUS consequences for the material involved in our research. if you are interested in records there are other records that can be possible like the 7th root of a 100 digit number, the 19th root of a 300 digit number, the 73rd root of a 1000 digit number, the 777th root of a 10000 or 12000-digit number and more possibilities...

for the competition with the 13th root, please send a message to

, the straightforward way to do it is with 100 digits there

Please do not rely on the Guinness Book that DOES NOT ACCEPT this as an official Guinness Record and which has published many mistakes about 13th roots so far.


World records

Time(seconds)#13th rootDatePlaceRecordholderNationalityWitness statements 1Witness statements 2
267.77 s 5772396280083911011 June 3rd, 2005 Paris, France Alexis Lemaire France Maitre AlbouLaurent Demonet


On April 6th, 2005, Alexis Lemaire from France became the first human to calculate mentally the 13th root of a 200-digit number, in front of official witnesses(especially the usher Maitre Albou) in an event organized by Science et Avenir. He took 513.55 seconds for the task #742, exactly 500 seconds more than his first world record in 13.55 seconds with 100 digits.


His correct answer was 2391481494636373
However, in the documentation, the first witness Jean Paul Delahaye was not careful enough and wrote a mistake in his own email address, so by applying the rules, the first record should not be validated.

On the 3rd of June in the same year, he needed only 267.77 seconds for the task #577 in the official conditions
and took only 113 seconds for the task #40 before the official starting, in the same conditions(in front of TF1 TV)

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 might multiply the difficulty by 10.

The 13th root of a 200-digit number has many kabbalistic or mystical potentials

the number 13 appears in judaism in particular:
in Shema Yisrael in Hebrew , the gematria of ONE is 13, a meaning of 13 is the monotheism (there is only ONE god) in hebrew letters.

The exact number of possibilities is:
3 935 44 3961 77 593

Rules for future world record attempts

  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 and HONEST mental calculation. It is NOT deceptive in any way, neither is it a matter of false difficulty. The difficulty is in the number of possibilities in the root(rather than the number of digits of the power), the order of the root, and the type of the root. 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
  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 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. Some record organizations like Guinness World Records can be even less reliable than the worst of the press, any record published or accepted by these organisations should not make any sense in the value of the record. These are no reliable authorities at all.
  27. 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
  28. 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.
  29. All the 13th roots from a 200-digit number correctly calculated must be included in the documentation, in an official group of attempts
  30. 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.
  31. The 2 witnesses MUST keep the sources codes and all the documentation
  32. 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.
  33. A special attention must be paid so that the fact that a random generator is not perfectly random can not help the mental calculation by any mean, for example by calculating mentally the value of the random functions from previous inputs/outputs.
  34. It is much preferable that the competitor does not use the computer program using the random generator before the event, and that the competitor does not practice with the random generator before the event.
  35. Any mean used to get some extra information from the answer other than through mental calculation can be interpreted as a fraud.

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