After a great deal of brow-furrowing and lip-chewing, he correctly calculated the answer to be 2,407,899,893,032,210.

Alexis Lemaire broke the world speed record yesterday for calculating the 13th root of a 200-digit number generated at random.

In other words, he worked out that the 16-digit solution above, when multiplied by itself 13 times, results in the number he was presented with — without using a calculator.

The French student achieved this extraordinary feat of mental arithmetic in just 70.2 seconds, beating his own previous record of 72.4 seconds.

After claiming his place in the Guinness Book of Records, 27-year-old Mr. Lemaire said: “When I do an extremely fast calculation, it is extremely satisfying. I’m really excited to improve myself. Since nobody else has done anything similar before, psychologically it is extremely rewarding.”

Calculating the 13th root of 100-digit numbers had been a goal for the world’s leading “mathletes” since a Herbert de Grote achieved the feat in 23 minutes in 1970. Mr. Lemaire, described as the world’s fastest human calculator, first claimed the record for that calculation in 2002.

He gave up the challenge three years ago after completing it in just 3.6 seconds.

Since then, he has concentrated on the far more difficult task of working out the 13th root of 200-digit numbers.

As a 9-year-old, he had impressed his friends and teachers by working out the square root of eight-digit numbers they tapped into calculators. He trains for about four hours a day, practicing calculations and memorizing thousands of tables of numbers and multiplications.

He said: “I will not say exactly what is my method. I am doing something like artificial intelligence in reverse, because I am imitating a computer.”

Mr. Lemaire, who is working on an artificial intelligence Ph.D. at the University of Reims, added that he believed it should be possible to achieve “mind uploading” —the hypothetical ability to create an accurate computer simulation of a human mind.

He added: “My ambition is to generalize these abilities to many brain processes, to run something like a computer program in my head, which I can use for any task. If I run a computer program all the time in my head, it should be possible to download it to a computer program. That leads to mind uploading. This would mean the computer would have all the same skills as me.”

He broke the record at the Science Museum in London.

The 13th root of a 200-digit number always begins with a two, whereas that for a 100-digit number always starts with a four.

A 13th root of a number will usually have approximately 1/13th the number of digits of the original. So the 13th root of a 100-digit number has eight digits, while that of a 200-digit number has 16 digits.

There are more than 3.9 trillion possible solutions for the 13th root of a 200-digit number.