The number 2018 is an even number, so in particular 2018 is not a prime number.
The prime factorization of 2018 is
\[2018=2\cdot 1009.\]
Here $2$ and $1009$ are prime numbers.

Identities for 2018

Here are some identities for 2018.

2018 is the sum of two squares

2018 is the sum of two squares:
\begin{align*}
2018=13^2+43^2.
\end{align*}
Here are some variants.
\begin{align*}
2018&=1^2+9^2+44^2\\
2018&=1^2+12^2+28^2+33^2\\
2018&=2^2+2^2+5^2+7^2+44^2\\
2018&=6^2+2(29)^2+3(10)^2
\end{align*}

2018 is a part of a Pythagorean triple

2018 is a part of a Pythagorean triple:
\begin{align*}
2018^2=1118^2+1680^2.
\end{align*}

This means that there is a right triangle whose hypotenuse is 2018.

Here are some variants.
\begin{align*}
2018^2&=18^2+88^2+2016^2\\
2018^2&=460^2+566^2+1172^2+1472^2\\
2018^3&=421^3+1490^3+1691^3
\end{align*}

2018 is the sum of 12 successive integers

2018 is the sum of 12 successive integers:
\[2018=7^2+8^2+9^2+10^2+11^2+12^2+13^2+14^2+15^2+16^2+17^2+18^2.\]

2018 appears in $\pi=3.14…$

2018 appears in the number $\pi=3.14…$ as in the following picture.

Mathematics About the Number 2017 Happy New Year 2017!!
Here is the list of mathematical facts about the number 2017 that you can brag about to your friends or family as a math geek.
2017 is a prime number
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The previous prime year was […]

Find the Largest Prime Number Less than One Million.
Find the largest prime number less than one million.
What is a prime number?
A natural number is called a "prime number" if it is only divisible by $1$ and itself.
For example, $2, 3, 5, 7$ are prime numbers, although the numbers $4,6,9$ are not.
The prime numbers have always […]

A One-Line Proof that there are Infinitely Many Prime Numbers
Prove that there are infinitely many prime numbers in ONE-LINE.
Background
There are several proofs of the fact that there are infinitely many prime numbers.
Proofs by Euclid and Euler are very popular.
In this post, I would like to introduce an elegant one-line […]

A Group with a Prime Power Order Elements Has Order a Power of the Prime.
Let $p$ be a prime number. Suppose that the order of each element of a finite group $G$ is a power of $p$. Then prove that $G$ is a $p$-group. Namely, the order of $G$ is a power of $p$.
Hint.
You may use Sylow's theorem.
For a review of Sylow's theorem, please check out […]

Each Element in a Finite Field is the Sum of Two Squares
Let $F$ be a finite field.
Prove that each element in the field $F$ is the sum of two squares in $F$.
Proof.
Let $x$ be an element in $F$. We want to show that there exists $a, b\in F$ such that
\[x=a^2+b^2.\]
Since $F$ is a finite field, the characteristic $p$ of the field […]

Even Perfect Numbers and Mersenne Prime Numbers
Prove that if $2^n-1$ is a Mersenne prime number, then
\[N=2^{n-1}(2^n-1)\]
is a perfect number.
On the other hand, prove that every even perfect number $N$ can be written as $N=2^{n-1}(2^n-1)$ for some Mersenne prime number $2^n-1$.
Definitions.
In this post, a […]

Beautiful Formulas for pi=3.14… The number $\pi$ is defined a s the ratio of a circle's circumference $C$ to its diameter $d$:
\[\pi=\frac{C}{d}.\]
$\pi$ in decimal starts with 3.14... and never end.
I will show you several beautiful formulas for $\pi$.
Art Museum of formulas for $\pi$ […]

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