Results 71 to 80 of about 131 (95)

Entropy Signatures and Spectral-Universality Heuristics in Goldbach Partitions

This revised preprint presents a computational and phenomenological analysis of Goldbach partitions through the combined lens of statistical physics and spectral theory. It examines Hardy–Littlewood singular-series structure, Shannon entropy signatures, congruence-sector behaviour, and finite-height spacing statistics of low-lying Riemann zeta ...
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Existence of Goldbach Partitions for Large Even Numbers under the 1/6 N Strong Constraint and a Rigorous Proof of the Order of Magnitude of the Goldbach Counting Function

This paper studies the counting function of even numbers expressed as sums of two primes. Using the 1/6N constraint and symmetric sieve method, we prove the discrete monotonicity of the counting function, which provides a new proof idea for Goldbach's Conjecture.
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A Geometric Construction for the Goldbach Conjecture: Sphere Helix Identity and Gauss Partition Method

Within the sphere helix framework of the Riemann ζ function (V12, DOI: 10.5281/zenodo.20504171), this paper establishes the exact algebraic identity cos(t_p) + cos(t_q) = 1/R, translating the Goldbach condition p + q = 2R into the dynamical language of the sphere helix. The 1/R on the right side comes entirely from V = 1/2 — the signature of
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Symmetric Goldbach Partition Theory: exact identities, unconditional bounds, and a demonstration program

I'm presenting the Symmetric Goldbach Partition Theory (SGPT), a framework reformulating Goldbach's conjecture via symmetric distances d around the midpoint m=N/2.  Main unconditional results:(1) Exact identity |T(m,z)|^2 = pi(z) + 2·CROSS(m,z), verified to N=10^12;(2) Selberg constant C_S = e^gamma/(2*C_2) = 1.34896, first ...
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A recursion relation for the number of Goldbach partitions of an even integer

Journal of Discrete Mathematical Sciences and Cryptography
The contour integral representation of the number of Goldbach partitions of an even integer, G(n), is extended to an integral with a support function that equals a linear combination of integers {G(m)}. A support function is found such that there is a nontrivial integral relation relating number of Goldbach partitions of n and m < n.
Simon Davis
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Deep learning-based approximation of Goldbach partition function

Discrete Mathematics, Algorithms and Applications, 2021
Goldbach’s conjecture is one of the oldest and famous unproved problems in number theory. Using a deep learning model, we obtain an approximation of the Goldbach partition function, which counts the number of ways of representing an even number greater than 4 as a sum of two primes.
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Goldbach partitions and sequences

Resonance, 2014
Properties of Goldbach partitions of numbers, as sums of primes, are presented and their potential applications to cryptography are described. The sequence of the number of partitions has excellent randomness properties. Goldbach partitions can be used to create ellipses and circles on the number line and they can also be harnessed for cryptographic ...
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Phenomenological Evidence of GUE Statistics and Thermodynamic Stability in Goldbach Partitions

This preprint presents a computational and phenomenological analysis of Goldbach's Conjecture through the combined lenses of spectral theory (GUE random matrix statistics) and statistical mechanics (thermodynamic entropy). Using an integral-refined Hardy–Littlewood heuristic with explicit Singular Series computation, we achieve convergence ratios of ≈1.
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An exact procedure for determining integers to be used in Goldbach partition and proof of Strong Goldbach conjecture

2021
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Exceptional zeros and the Goldbach problem

Journal of Number Theory, 2022
J B Friedlander, Daniel A Goldston, H Iwaniec   +2 more
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