A mathematical duo has made a surprising advance in understanding the distribution of prime numbers, those whole numbers divisible only by themselves and 1. The new result is the most exciting work on prime numbers in more than 3 decades, says mathematician Hugh L. Montgomery of the University of Michigan in Ann Arbor.
However, he cautions that experts are still checking the details of the proof.
Among small numbers, primes are common. Of the first 10 numbers, for instance, 4 of them–2, 3, 5, and 7–are prime. But among larger numbers, primes thin out. Around a trillion, for instance, only about 1 in every 28 numbers is prime.
In the late 19th century, mathematicians proved that the distribution of primes follows an amazingly simple pattern: The average spacing between primes near a number x is the natural logarithm of x, a number closely related to the number of di