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?
Best Answer
The outer $\pi$ is the prime-counting function.