Mathematicians like to classify and organize numbers in all kinds of ways. Natural numbers are used for counting and ordering; nominal numbers are used for naming (like a driver’s license number); integers are numbers that can be expressed without a fraction or decimal; prime numbers can only divided by 1 and by themselves; and so on. But there is no limit to how we can understand and use numbers; accordingly, there is a branch of pure mathematics, primarily based upon the study of integers, called “number theory.” Though we now understand that number theory has boundless applications, uses, and purposes, it can appear to be frivolous to the point of pointlessness – especially the subset known as “recreational number theory.” Number theorist Leonard Dickson once said, after all, “Thank God that number theory is unsullied by any application.”

Melissa & Doug Abacus ... Buy New $12.50 (as of 08:45 UTC - Details) But that doesn’t mean it doesn’t provide a measure of nerdy fun for those so inclined. Read on to learn what makes a number “interesting,” “weird,” “happy,” “narcissistic,” “perfect,” and more!

10 Amicable numbers

Ah, amicable numbers. They love each other so much. How much? Well, let’s take a classic pair—284 and 220—and see just how friendly they are. Let’s take all the proper divisors of 220 (that is to say, all its divisors that leave no remainder, including the number 1, and excluding the number itself) and all them up:

1 + 2 + 4 + 5 + 10 + 11 + 20 + 22 + 44 + 55 + 110 = 284 Fibonacci Fun: Fascina... Trudi Hammel Garland Best Price: $17.19 Buy New $116.81 (as of 08:55 UTC - Details)

Now, let’s take 284 and do the same thing:

1 + 2 + 4 +71 + 142 = 220.

Voila: a pair of amicable numbers. Other pairs include (1184, 1210), (2620, 2924), and (5020, 5564). This type of number pair was discovered and studied by the Pythagoreans, and has been the subject of much research through the centuries – Fermat, Descartes, My Best Mathematical a... Gardner, Martin Best Price: $1.81 Buy New $4.16 (as of 12:10 UTC - Details) Iranian Muhammad Baqir Yazdi, and Iraqi Th?bit ibn Qurra are among the many mathematicians who have delved into the world of amicable numbers. Topics of further study include attempts to discover if there is an infinite amount of pairs, to discern patterns, and to better understand why and how this happens.

Because mathematicians would never be satisfied with mere amicable numbers, “betrothed numbers” are pairs where the sum of the proper divisors of each number is equal to the other number +1.

9 Emirp

“Emirp” is the word “prime” spelled backwards, and it refers to a prime number that becomes a new prime number when you reverse The Moscow Puzzles: 35... Kordemsky, Boris A. Best Price: $2.30 Buy New $7.00 (as of 11:45 UTC - Details) its digits. Emirps do not include palindromic primes (like 151 or 787), nor 1-digit primes like 7. The first few emirps are 13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 149, and 157 – reverse them and you’ve got a new prime number on your hands.

Mostly, saying “emirp” over and over is kind of a blast. Give it a whirl!

8 Interesting Numbers

There is an old paradox in the world of mathematics that is known as the “interesting number paradox.” Simply put, if you keep counting natural numbers, eventually you’ll encounter one that isn’t interesting; where it gets paradoxical is that by virtue of being the smallest uninteresting number, that number has now become interesting.

Of course, this is all subjective, as it relies on a vague definition of the word “interesting.” Very generally speaking, a number is considered interesting if it has some type of mathematical quality that sets it apart; 19 is interesting because it’s prime, 999 is interesting because it’s a palindrome (and the UK version of 911); 24 is interesting because (among other reasons) it’s the largest number divisible by all numbers less than its square root. Mathematicians.

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