as the atoms of arithmetic, prime numbers have always occupied a special place on the number line. Now, Jared Duker Lichtman, a 26-year-old graduate student at the University of Oxford, has resolved a well-known conjecture, establishing another facet of what makes the primes special—and, in some sense, even optimal. “It gives you a larger context to see in what ways the primes are unique, and in what ways they relate to the larger universe of sets of numbers,” he said.
The conjecture deals with primitive sets—sequences in which no number divides any other. Since each prime number can only be divided by 1 and itself, the set of all prime numbers is one example of a primitive set. So is the set of all numbers that have exactly two or three or 100 prime factors.
Primitive sets were introduced by the mathematician Paul Erdős in the 1930s. At the time, they were simply a tool that…
