C. Wilson

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math.NT2020

On coefficients satisfying Chebyshev's approximation of $π (x)$

Connor Paul Wilson

We note an interesting and under-expressed fact from Chebyshev's initial bounding for the prime counting function, $π (x) := # {p \leq x : p prime},$ based upon a selecti…

math.NT2020

Estimates of the bounds of $π (x)$ and $π ((x + 1)^{2}) - π (x^{2})$

Connor Paul Wilson

We show the following bounds on the prime counting function $π (x)$ using principles from analytic number theory, giving an estimate: $$2 \log 2 \geq \limsup_{x \rightarrow \infty}…

On coefficients satisfying Chebyshev's approximation of π(x)

Estimates of the bounds of π(x) and π((x+1)2)−π(x2)

On coefficients satisfying Chebyshev's approximation of $π (x)$

Estimates of the bounds of $π (x)$ and $π ((x + 1)^{2}) - π (x^{2})$