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.

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

As Wolfram MathWorld explains, a prime number – also known simply as a prime – is a positive number greater than 1 that can only be divided by the one and itself.

"The only even prime number is 2," explains Debi Mink, a recently retired associate professor of education at Indiana University Southeast, whose expertise includes teaching elementary mathematics. "All the other primes are odd numbers."

Numbers like 2, 3, 5, 7, 11, 13 and 17 are all considered prime numbers. Numbers like 4, 6, 8, 9, 10 and 12 are not.

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.)

"Think about the number 6," says Zegarelli, citing a composite number. "Imagine that you have six coins. You could form them into a rectangle, with two rows of three coins. You can do that with eight, too, by putting four coins into two rows. With the number 12, you could make it into more than one type of rectangle — you could have two rows of six coins, or three times four. "

"But if you take the number 5, no matter how you try, you can't put it into a rectangle, " Zegarelli notes. "The best you can do it is string it into a line, a single row of five coins. So, you could call 5 a non-rectangular number. But the easier way to say that is to call it a prime number. "

There are plenty of other primes — 2, 3, 7 and 11 also are on the list, and it keeps rolling from there. The Greek mathematician Euclid, back in circa 300 B.C.E., devised a Proof of the Infinitude of Primes, which may have been the first mathematical proof showing that there is an infinite number of primes. (In ancient Greece, where the modern concept of infinity wasn't quite understood, Euclid described the quantity of primes simply as "more than any assigned multitude of prime numbers.")

Another way of understanding primes and composite numbers is to think of them as the product of factors, Zegarelli says. "2 times 3 equals 6, so 2 and 3 are factors of 6. So, there are two ways to make six — 1 times 6, and 2 times 3. I like to think of them as factor pairs. So, with a composite number, you have multiple factor pairs, while with a prime number, you have only one factor pair, one times the number itself. "

Proving that the number of primes are infinite isn't that tough, Zegarelli says. "Imagine that there is a last, biggest prime number. We're going to call it P. So then I'll take all the prime numbers up to P and multiply them all together. If I do that and add one to the product, that number has to be a prime. "

If a number is a composite, in contrast, it's always divisible by some quantity of lower prime numbers. "A composite could be divisible by other composites as well, but eventually, you can decompose it down to a set of prime numbers. " (An example: the number 48 has 6 and 8 as factors, but you can break it down further into 2 times 3 times 2 times 2 times 2.)

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