bolton8l

2022-10-08

Proof that $lim\left(\vartheta \left(x\right)-x\right)\ne 0?$ ?

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Farbwolkenw

Expert

does not exist. We can prove it by contradiction.
If exists, then

It means that
If there is a prime in $\left(x,x+1\right]$, then $\sum _{x\mathrm{log}x$, if there is no prime in $\left(x,x+1\right]$, then $\sum _{x, so cannot exist, it contradicts with the previous, so cannot exist.

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