For the Easily Amused: Is Your Telephone Number a Prime Number?

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Bored? At least moderately nerdy? If trolling YouTube for videos of solo-guitar renditions of classic video game theme music has lost its luster, you could waste a couple minutes determining if your 10-digit telephone number is prime. 

(For those of us who had social lives in high school and may have missed this unit, a positive whole number is said to be prime if it can be divided evenly only by itself and 1. In order of appearance, the primes are 2, 3, 5, 7, 11, 13, 17, and so on.)

Primes hold a special place in the hearts of the mathematically obsessed. On the one hand, there are an infinite number of primes, which means there are always some yet waiting to be discovered. On the other hand, they become increasingly rare as you travel along the number line, which makes large prime numbers especially precious. A 10-digit telephone number, for example, has a little less than a 1-in-20 chance of being prime. Let’s cut the chit-chat and see if you’ve won the prime telephone number lottery:

First, examine the last digit. If it’s an even digit (0, 2, 4, 6, or 8), you’ve already been eliminated because your telephone number is divisible by 2 at the very least. If it’s a 5, same sad story—it’s definitely divisible by 5. (My telephone number ends in a 7, so I was fairly hopeful at this point.)

If you’ve made it this far, your chances have increased to better than 1-in-10. If you’ve already been cut, take heart—you’re in good company.

Next, add the digits of your telephone number together. If what you get is divisible by 3, then so is your telephone number, and you’re out. (The sum of the digits of my phone number is 41. So far, so good.)

If your number is still a contender, visit this simple prime number test devised by the good folks at the University of Southern Indiana. Input your telephone number and click on the “Check My Number” button. (At this step I was grieved to discover that my telephone number is not prime, but is in fact the product of two rather large prime numbers, 14,629 and 280,583. Call me.)

If you won the prime telephone number lottery, congratulations… I guess. If your number didn’t make the cut, you can always test your Social Security number, your birth year, your BGE account number, the list goes on and on.

And remember, if you cheat and skip to the last step, then the whole exercise doesn’t really waste enough time, which is, of course, its primary purpose.



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