Interesting ways to write 2023 The year 2023 is near and today I found this nice way to write that number:
$\displaystyle\color{blue}{\pi}\left(\frac{(\pi !)!-\lceil\pi\rceil\pi !}{\pi^{\sqrt{\pi}}-\pi !}\right)+\lfloor\pi\rfloor=2023$
where $\color{blue}{\pi}$ is the counting function of prime numbers.
My question is, do you know any other interesting way to write 2023?
By the way, happy new year everyone
 A: $2023$ is a sum of four squares (but not of fewer ones), e.g.,
$$
2023=10^2+11^2+11^2+41^2.
$$
It is also the sum of three cubes, e.g.,
$$
2023=2^3+(-9)^3+14^3.
$$
It is sort of close to $111111111111$ in the binary system.
$$
2023=11111100111.
$$
A: You writing $2023$ using only $\pi$ and this video from Presh Talwalkar inspired me to give this representation of $2023$ as an answer:
$$2023=\frac{\ln({\frac{\ln(\pi)}{\ln(a)}})}{\ln(-\cos(\pi)-\cos(\pi))},$$
$$a=\pi^{\frac{1}{b}},b=2^{2023}.$$
This discussion on Puzzling Stack Exchange is worth checking out as well.
A: $$2023=\lfloor (45-\frac{1}{45})^2\rfloor$$
A: $$(2+0+2+3)(2^2 + 0^2 + 2^2 + 3^2)^2 = 2023$$
A: $$2023=\Big(\frac{2^3+3^2}{2^{10}3^2}\Big)\phi(2022)\phi(2023)$$
where $\phi$ is Euler's totient function.
A: $$9^3+8^3+7^3+6^3+5^3+4^3+3^3+2^3-1^3=2023$$
A: So close to $2^{10} + 10^3$.
$$2023 = 2^{10} + 999$$
A: \begin{array}{}
20 \cdot 2^{3} \quad + \quad 23 \cdot 3^{2^{2}}\\
\end{array}
A: There are total $\left(\dfrac{3\times3\times2\times1}{2!}\right)=9$ four-digit significant numbers, formed by permuting the four digits $\color{red}{2},\color{red}{0}, \color{red}{2}, \color{red}{3}$ without repetition, which can be arranged in ascending order as follows
$$\begin{pmatrix} 
\color{red}{2023}\\
2032\\
2203\\2230\\2302\\2320\\3022\\3202\\3220
\end{pmatrix}$$
The rank of $\color{red}{2023}$ in the ascending order in its table is $\color{blue}{1}$.
A: $45^{2}-2=2023$
$2^{11}-5^2=2023$
$2^{8}+12^{3}+39=2023$
$3^6+6^4-2=2023$
$3+4\cdot5+40\cdot50=2023$
Let $P_{n}$ denotes the nth prime,then:
$ 35+\sum_{n=1}^{33} P_{n} =2023 $
$ -104+\sum_{n=1}^{34} P_{n} =2023 $
I wish great happy new year for all people.
A: Thanks to Wolfram Alpha
$$2023 \sim \frac A{11^2} $$  where
$$A=18468 \binom{\pi }{\pi !}+5548 \binom{\pi !}{\pi }+8724
   \binom{\pi !}{\log (\pi )}-19734 \binom{\log (\pi )}{\pi
   !}-$$ $$15884 \binom{\pi }{\log (\pi )}-4309 \binom{\log (\pi
   )}{\pi }$$
The difference between rhs and lhs is $3.42 \times 10^{-28}$.
A: We have
$$\require{cancel} \sum_{n=1}^{2+0+2+3}\left(1+\frac{2.\cancel{0}.2.3}{\cancel{0}}[n+1]n\right)=2023$$
A: Just keep it simple
$$ \int_0^1 x^{2022} \, \mathrm{d}x = \frac{1}{2023} $$
And I know one more cool integral which is
$$ \int_0^\infty \frac{\tan^{-1}(2022 x)}{x(x^2+1)} \mathrm{d}x = \frac{\pi}{2} \ln(2023) $$
A: $$2023 = ((( 9\times 8\times 7) +2 ) \times 4 ) –  ( 5+3) +  ( 6 + 1 + 0)$$
(i.e., using all digits exactly once)
A: $\text{2022}$+$\text{1}$=$\text{2023}$
A: A palindromic hexadecimal number:
$$2023_{10} = 7e7_{16}$$
A: $2023$ can be written as
$$\text{the year you were born}+\text{how many years old you are}+1$$
This works $100\%$ of the time when this calculation is performed at the very beginning of $2023$.
A: Addition of the place values:
$$\Large \color{red}{2023}=\large \color{red}{2}\cdot 1000+\color{red}{0}\cdot 100+\color{red}{2}\cdot 10+\color{red}{3}\cdot 1$$
A: Something easy :
$$2023+3202=5225$$
Wich is palindromic too .
A: This isn't exactly what you're after, but it's my personal new year announcement:

