Register for an account

X

Enter your name and email address below.

Your email address is used to log in and will not be shared or sold. Read our privacy policy.

X

Website access code

Enter your access code into the form field below.

If you are a Zinio, Nook, Kindle, Apple, or Google Play subscriber, you can enter your website access code to gain subscriber access. Your website access code is located in the upper right corner of the Table of Contents page of your digital edition.

The Sciences

Picky Primes

A discovery that shocked mathematicians.

By Julie RehmeyerDecember 21, 2016 6:00 AM
shutterstock_152874113.jpg
Robert Lessmann/Shutterstock

Newsletter

Sign up for our email newsletter for the latest science news

Prime numbers — those that are divisible only by 1 and themselves — aren’t quite as random as mathematicians thought. In particular, they seem to have definite preferences about the final digits of the primes that follow them.

Primes especially dislike following primes with the same final digit as their own. Among the first billion primes, for example, primes ending in 9 follow a prime also ending in 9 only 60 percent as often as they follow a prime ending in 1.

In a paper submitted in March, Kannan Soundararajan of Stanford University and Robert Lemke Oliver of Tufts University showed that the pattern holds among the first 400 billion primes and offered a possible explanation for it. The tendency diminishes as primes get bigger, but only very slowly.

The discovery shocked mathematicians, because a fundamental understanding about prime numbers is that they behave much like random numbers, without orderly patterns in their distribution. The new information shows that this randomness is more complicated than had been believed.

2 Free Articles Left

Want it all? Get unlimited access when you subscribe.

Subscribe

Already a subscriber? Register or Log In

Want unlimited access?

Subscribe today and save 70%

Subscribe

Already a subscriber? Register or Log In