Carmichael numbers math proof found by US teenager

Daniel Larsen ticked a little differently as a 13-year-old: the teenager from Bloomington in the US state of Indiana loved to puzzle over puzzles like Scrabble – a game that has been known more for its elderly fans since Loriot’s “Schwanzhund” at the latest – and even created his own crossword. He sent them to major newspapers, including the New York Times (NYT). Eight times he tried. And eight times he was kindly told that his riddles didn’t really suit the readership: too difficult, the words he was looking for too unfamiliar. Not discouraged by this, however, he wrote a computer program that helped him improve his puzzle. The ninth submission then brought the long-awaited success: Larsen became the youngest puzzler in NYT history in 2017.

Stubborn perseverance coupled with an almost tireless tolerance for frustration: Daniel Larsen already amazed people as a child. Last summer, now 17 and in his senior year of high school, these traits enabled him to produce a complicated proof from number theory: he was able to show that there is always a Carmichael number in the interval between x and 2x are. Here, x represents any natural number that is sufficiently large. Carmichael numbers are objects that are also called pseudoprimes because they satisfy certain relations that apply to prime numbers without actually being prime numbers.

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