Leider weiß ich nicht, wie ich hier eine Exceltabelle mit den Formeln und der Primzahlrechnung hochladen kann, bzw. ob es möglich ist. Ich bin sehr dankbar für Antworten!
English Translation (via Google Translate):
Title: Would it be an improvement to calculate the number of primes (quantity) up to a selected size or is it already known?
Body: Unfortunately, I do not know how to upload an Excel spreadsheet with the formulas and the prime number calculation, or whether it is possible. I am very grateful for answers!
The prime counting function $$ \pi(x)=\sum_{p\le x} 1 $$ has been computed up to $$ \pi(10^{27})=16,352,460,426,841,680,446,427,399. $$ by David Baugh and Kim Walisch in $2015$, see here. Your list therefore should start there, to be possibly better. For the history of computing $\pi(x)$ see the article A computational history of prime numbers and Riemann zeros.
By the way, for some errors in the estimation of $\pi(x)$, which keep showing up in some books and papers, see my article A remark on an inequality for the prime counting function.