# Is this $2020$ holiday formula correct? $\pi\left( \dfrac{\left( \pi!\right)!-\lceil \pi \rceil \pi! }{{\pi}^{\sqrt \pi}-\pi!}\right)=2020$

I found the following formula in another math group:

$$\large\color{blue}{\pi\left( \dfrac{\left( \pi!\right)!-\lceil \pi \rceil \pi! }{{\pi}^{\sqrt \pi}-\pi!}\right)=2020}$$

It actually looks very "elegant". But, then I used Wolfram because I was in doubt.. The result shows that this formula is wrong.

I wrote these steps:

$${\qquad \quad \color{red}{\pi\left( \dfrac{\left( \pi!\right)!-\lceil \pi \rceil \pi! }{{\pi}^{\sqrt \pi}-\pi!}\right)=\color{blue}{\dfrac {\pi \Gamma(1 + \Gamma(1 + \pi))-4 \pi \Gamma(1 + \pi))}{{\pi}^{\sqrt \pi} - \Gamma(1 + \pi)}}\color{red}{\approx55221,71}}\color{blue}{\neq2020}}$$

My questions are:

• I wonder if there is a small typo in the formula?
• Or is the formula far from accurate in any case?

The outer $$\pi$$ is the prime-counting function.
• Or, $\pi(17577.6)=2020$ – QC_QAOA Jan 1 at 21:13
• In Mathematica, PrimePi[17577.61614280863]=2020 – Pixel Jan 1 at 21:13