Empirical verification of the even Goldbach conjecture and computation of prime gaps up to 4⋅10¹⁸

DOI10.1090/S0025-5718-2013-02787-1zbMath1290.11161OpenAlexW2034249254WikidataQ29302883 ScholiaQ29302883MaRDI QIDQ5418501

Silvio Pardi, Siegfried Herzog, Tomas Silva

Publication date: 4 June 2014

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-2013-02787-1

zbMATH Keywords

prime gapsGoldbach conjectureprime \(k\)-tuple conjecture

Mathematics Subject Classification ID

Goldbach-type theorems; other additive questions involving primes (11P32) Distribution of primes (11N05) Primes (11A41) Computational number theory (11Y99) Sieves (11N35)

Related Items

On multiplicative functions with \(f(p+q+n_{0})=f(p)+f(q)+f(n_{0})\), Classification and counting of planar quasi-homogeneous differential systems through their weight vectors, Curves on the torus intersecting at most k times, Large gaps between consecutive prime numbers, Finite connected components of the aliquot graph, Refined Goldbach Conjectures with Primes in Progressions, On the sum of a prime and a square-free number, Explicit interval estimates for prime numbers, Long gaps between primes, Deep learning-based approximation of Goldbach partition function, Summing \(\mu(n)\): a faster elementary algorithm, On the error term in the explicit formula of Riemann–von Mangoldt, Multiplicative functions with $f(p+q-n_0) = f(p)+f(q)-f(n_0)$, Computers as a novel mathematical reality. IV: The Goldbach problem, Explicit estimates of some functions over primes, On the sum of a prime and a square-free number with divisibility conditions, The sequence of prime gaps is graphic, An exploration of Nathanson's \(g\)-adic representations of integers, Asymptotics of Goldbach representations, Additive uniqueness of PRIMES − 1 for multiplicative functions, Primes between consecutive powers, Unnamed Item, On Grosswald’s conjecture on primitive roots, On the first occurrences of gaps between primes in a residue class, Two Independent Checkings of the Weak Goldbach Conjecture up to 10²⁷, Some problems of Erdős on the sum-of-divisors function, Primes in explicit short intervals on RH, Inductive formulas related to prime partitions, Empirical significance, predictive power, and explication, An improved sieve of Eratosthenes, Fourier optimization and prime gaps

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A space-efficient fast prime number sieve
• Exceptional set of Goldbach number
• Explaining the wheel sieve
• Short effective intervals containing primes
• Verifying the Goldbach conjecture up to 4⋅10¹⁴
• Every odd number greater than $1$ is the sum of at most five primes
• Gaps between primes, and the pair correlation of zeros of the zeta-function
• Fast compact prime number sieves (among others)
• Computing π(x): The Meissel-Lehmer Method
• First Occurrence Prime Gaps
• A note on Goldbach's conjecture
• Numerical results on the Goldbach conjecture
• On the distribution of primes in short intervals
• The segmented sieve of eratosthenes and primes in arithmetic progressions to 1012
• New maximal prime gaps and first occurrences
• Checking the Goldbach Conjecture up to 4 ⋅10 11
• A complete Vinogradov 3-primes theorem under the Riemann hypothesis
• Checking the odd Goldbach conjecture up to 10²⁰
• Prime sieves using binary quadratic forms
• Jumping Champions
• On the Vinogradov bound in the three primes Goldbach conjecture
• Counting primes in residue classes
• Harald Cramér and the distribution of prime numbers
• Computing 𝜋(𝑥): the Meissel, Lehmer, Lagarias, Miller, Odlyzko method
• The Distribution of Small Gaps Between Successive Primes
• Laguerre's Method Applied to the Matrix Eigenvalue Problem
• Averages of Euler products, distribution of singular series and the ubiquity of Poisson distribution
• On checking the Goldbach conjecture
• Experimental Results on Additive 2-Bases
• The First Occurrence of Large Gaps Between Successive Primes
• The General Form of the So-Called Law of the Iterated Logarithm
• Unsolved problems in number theory