by **Guest** » Thu Mar 01, 2018 1:21 pm

Guest wrote:The question is stronger than the related Legendre's Conjecture (https://en.wikipedia.org/wiki/Legendre%27s_conjecture).

And the key result is:

[tex]\pi((n+1)^{2})[/tex] - [tex]\pi(n^{2})[/tex] [tex]\rightarrow[/tex] [tex]\pi(n)[/tex] = n/log(n) as [tex]n \rightarrow \infty.[/tex]

Example: [tex]\pi(75,001^{2})[/tex] - [tex]\pi(75,000^{2})[/tex] - [tex]\pi(75,000)[/tex]

= (262,872,577 - 262,865,922) - 7493

= 6755 - 7493 = -738 (almost 11% error);

6755 - 75,000/log(75,000) = 6755 - 6681

= 74 (almost 1% error).

Those excellent results correspond very well with our theory!

Dave the antworker