The French artificial intelligence student achieved the 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, Mr Lemaire said: "When I do an extremely fast calculation 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 has been a yardstick for the world's leading "mathletes" since a Herbert B. de Grote achieved the feat in 23 minutes in 1970.
Mr Lemaire first claimed that record in 2002 but gave up the challenge three years ago after completing it in 3.6 seconds. Since then he has concentrated on more difficult 200-digit numbers.
As a nine-year-old he used to impress his school friends and teachers by working out the square root of eight-digit number they tapped into calculators.
He trains for around four hours per day, practising calculations and memorising thousands of tables of numbers and multiplications.
Mr Lemaire, who will not reveal precise details of how he does it, describes the process as "reverse artificial intelligence".
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 PhD 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 generalise these abilities to many brain processes, to run something like a computer programme in my head which I can use for any task.
"If I run a computer programme all the time in my head, it should be possible to download it to a computer programme and that leads to mind-uploading.
"This would mean the computer would have all the same skills as me. I think it is possible."
He broke the record at the Science Museum in London, against a backdrop of Charles Babbage's Difference Engine No. 2 - the world's first successful mechanical calculator, designed in the 1840s.
Jane Wess, curatoe of mathematics at the museum, said: 'He sat down and it was all very quiet and all of a sudden he just cracked it.
'He seems to have a large memory and he's made this his life ambition. It's quite remarkable to see it happen.'
Please click on video
The Daily Telegraph