There’s a New Way to Count Prime Numbers

The original version of this story appeared in Quanta Magazine. A new proof has brought mathematicians one step closer to understanding the hidden order of those “atoms of arithmetic,” the prime numbers. By showing that there are still infinitely many primes that satisfy such increasingly rigid constraints, they’ve been able to learn more about where the primes live. “It really surprised me that they did this.” A Trying Set Mathematicians tend to study families of primes that are just complicated enough to be interesting but still simple enough to make progress on. They might try to prove, for instance, that there are infinitely many primes that are 500 units apart.