6

For all its ups and downs as a year, 2017 is a prime number. However, after midnight, the year is 2018. It is not a prime number! It is also...

  • not a fibonacci number
  • not a Bell number
  • not a perfect number
  • not a factorial
  • not a catalan number

...and so on. The only good thing Wolfram Alpha has to say about $2018$ is that it's a divisor of $87^{18} - 1$, but I see nothing special about that.

So please help me out: What is the best thing to toast to when 2018 arrives?

naslundx
  • 9,896

7 Answers7

15

Every natural number is the sum of four integer squares, but 2018 is:

$$2018=(6^2)^2+(5^2)^2+(3^2)^2+(2^2)^2$$ the sum of four squares of squares.

11

Someone born that year will be having their 30 years party in $2048 = 2^{11}$ which is probably the only power-of-two any of us will live to see.

mathreadler
  • 26,534
11

There is exactly one non-abelian group of order $2018$ by the Sylow-Theorems. There are exactly 2018 duplicates of this here at MSE:

Nonabelian group of order $pq $

Groups of order $pq$ are cyclic

Group of order pq is not simple

Question about soluble and cyclic groups of order pq

$\cdots $

$\cdots$

Non Abelian group of order pq

Dietrich Burde
  • 140,055
6

Well, I should say that Even What’s Special About This Number has no result for the number $2018$...

Zsbán Ambrus
  • 310
  • 3
  • 18
  • 1
    Wow, speciality of $2017$ is not only being prime, I did not know that $2017$ has such speciality as being the value of $n$ with $\phi(n) = \phi(n-1)+\phi(n-2)$. I am sure in some Math Olympiad, the question "Find the value of $n$ that satisfies $\phi(n) = \phi(n-1)+\phi(n-2)$" is asked in this year :D – ArsenBerk Dec 31 '17 at 12:01
  • For a moment I thought you are talking about the number 2018!! and I wondered how in the world did somebody analyze that huge number – Stefan4024 Dec 31 '17 at 12:41
  • 1
    @Stefan4024 Well, that was unintentional.... –  Dec 31 '17 at 12:41
5

If there is a special name for the even numbers of the form $2p$, where $p$ is a prime number, then $2018 = 2\cdot 1009$ where $1009$ is a prime number.

The closest thing that I found is the numbers called "Safe Numbers" which is in the form of $2p+1$: https://en.wikipedia.org/wiki/Safe_prime

ArsenBerk
  • 13,388
4

Ramanujan-Nagell equation is exponential Diophantine equation of the form $$2^n-7=x^2$$

When I searched for squares close to $2018$ I discovered that we have $$2018=45^2-7$$ and then I observed that $2018$ is a solution of Diophantine equation

$$2^n+2^{n-1}+...+2^5+2=x^2-7$$

for $n=10$ and $x=45$, which is one of myriad of possible generalizations of Ramanujan-Nagell equation.

2

We can look forward to less evil, at least. 2017 is a very evil number. I have two proofs of this.

  1. Note that 5 is the number of Satan and that "derangement" is a nasty word. How many derangements are there of 5? 44. So 44 is evil compounded. Also note that we had this nice pattern: 3, 5, 7, ... where all the odds were prime. What screwed it up? 9. Evil, evil 9. Is it any wonder that Christ died "at the 9th hour?" So we have 9 and 44, already evil compounded. Let's re-compound them by squaring and re-re-compound them by adding the results:

$$9^2+44^2 = 2017.$$

Chilling, no? There's more"

  1. We know that gambling is evil and in craps the phrase is "7, 11 or doubles." To get "doubles" let's take 7 twice: 7, 7, 11. There's a multi-set of evil. Let's super-compound them by cubing (and note that dice are cubes!) and add:

$$7^3+7^3 + 11^3 = 2017.$$

Thankfully, there are only a few hours left in this horrible year. Let's hope we make it to 2018.

B. Goddard
  • 33,728