New estimates for the $n$th prime number

zbMath1418.11130arXiv1706.03651MaRDI QIDQ5377966

Christian Axler

Publication date: 11 June 2019

Full work available at URL: https://arxiv.org/abs/1706.03651

zbMATH Keywords

prime numberprime counting functionChebyshev's \(\theta\)-function

Mathematics Subject Classification ID

Distribution of primes (11N05) Primes (11A41)

Related Items (5)

On Ramanujan primes ⋮ Error estimates for a class of continuous Bonse-type inequalities ⋮ On the sum of the first \(n\) prime numbers ⋮ The Erdős conjecture for primitive sets ⋮ Unnamed Item

Uses Software

• OEIS

Cites Work

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• Fast computation of some asymptotic functional inverses
• Explicit estimates of some functions over primes
• Effective bounds for certain functions concerning prime numbers
• Estimates of the \(k\)th prime under the Riemann hypothesis
• The \(n\)-th prime asymptotically
• Approximate formulas for some functions of prime numbers
• Estimating $\pi (x)$ and related functions under partial RH assumptions
• Estimation de la fonction de Tchebychef θ sur le k-ième nombre premier et grandes valeurs de la fonction ω(n) nombre de diviseurs premiers de n
• Sharper Bounds for the Chebyshev Functions θ(x) and ψ(x)
• The 𝑘^{𝑡ℎ} prime is greater than 𝑘(ln𝑘+lnln𝑘-1) for 𝑘≥2
• Proof of the Sheldon Conjecture
• New estimates for some functions defined over primes

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