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Monday, April 05, 2021

What Are Prime Numbers, and Why Do They Matter? | Math Concepts - HowStuffWorks

Patrick J. Kiger, HowStuffWorks observes, You may remember from math class that a prime number is a number that can only be divided by 1 and itself. But why are they important anyway?

What do these numbers have in common? They're all prime!
Photo: geralt/Pixabay

If you only vaguely remember your elementary school mathematics class, you may not remember what a prime number is. That's a pity, because if you're trying to keep your emails safe from hackers or surf the web confidentially on a virtual private network (VPN), you're using prime numbers without even realizing it.

That's because prime numbers are a crucial part of RSA encryption, a common tool for protecting information, which uses prime numbers as keys to unlock the messages hidden inside gigantic amounts of what's disguised as digital gibberish. Additionally, prime numbers have other applications in the modern technological world, including an important role in defining the color intensity of the pixels on the computer screen that you're staring at now.

So, what are prime numbers, anyway? And how did they get to be so important in the modern world?...

Mark Zegarelli, author of numerous books on math in the popular "For Dummies" series who also teaches test prep courses, offers an illustration involving coins that he uses with some of his students to explain the difference between primes and composite numbers, which can be divided by other numbers besides one and themselves. (Composite numbers are the opposite of primes.)...

That's why mathematicians have continued to labor to come up with increasingly bigger primes, in an ongoing project called the Great Internet Mersenne Prime Search. In 2018, that project led to the discovery of a prime number that consisted of 23,249,425 digits, enough to fill 9,000 book pages, as University of Portsmouth (England) mathematician Ittay Weiss described it in The Conversation. It took 14 years of computations to come up with the gigantic prime, which is more than 230,000 times bigger than the estimated number of atoms in the observable universe!

You can imagine how impressed Euclid might be by that.

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Source: HowStuffWorks