We have completed maintenance on DiscoverMagazine.com and action may be required on your account. Learn More

Picky Primes

A discovery that shocked mathematicians.

By Julie Rehmeyer
Dec 21, 2016 6:00 AMNov 12, 2019 6:14 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.

1 free article left
Want More? Get unlimited access for as low as $1.99/month

Already a subscriber?

Register or Log In

1 free articleSubscribe
Discover Magazine Logo
Want more?

Keep reading for as low as $1.99!

Subscribe

Already a subscriber?

Register or Log In

More From Discover
Recommendations From Our Store
Shop Now
Stay Curious
Join
Our List

Sign up for our weekly science updates.

 
Subscribe
To The Magazine

Save up to 40% off the cover price when you subscribe to Discover magazine.

Copyright © 2024 Kalmbach Media Co.