Under the eye of official timekeepers, Alexis Lemaire, 24, a computer science student from Reims, took 513 seconds to find the 16-digit number which, multiplied by itself 13 times, produced a 200-digit sequence that had been presented to him on a computer screen. He was not allowed to write or type.

Thirteenth roots have long been used as the test for records. The figure is chosen because 13 is a prime number whose roots cannot be obtained by combining those of other numbers.

M Lemaire, a shy, bearded student, amazed mental mathematicians in December when he beat the record held by a German, Gert Mittring, for finding the 13th root of a 100-digit number. He did so in 3.62 seconds, against Herr Mittring’s 13.55.

M Lemaire had been practising two hours a day since December for the 200-digit challenge by memorising numbers that were powers of 13. “This is the most difficult mental calculation in the world,” he said after his test, which was organised by Sciences et Avenir magazine. “It is 100 times more difficult than the record I broke in December because this time there was only a one in 400,000 billion chance of getting the result by luck against 1 in 8 million in December.”

Before the challenge, Robert Fountain, a prizewinning mental calculator from Northwich, Cheshire, was quoted on the 13th root internet site as saying: “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.”

According to neurological scientists at Caen University, genius arithmeticians use a different part of the brain from that used by average humans.

M Lemaire, who is learning 40 languages simultaneously in his spare time, has promised to reveal part of his technique. His favourite numbers are 13, 67 and 37. Would-be challengers are being directed to the website www.13throot.com

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