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The Superiority of Hilbert Arithmetic for Prime Number Theory: I Goldbach's conjecture proved in Hilbert arithmetic

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Chebyshev's Bias
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The sheaf-theoretic structure of non-locality and contextuality
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Long gaps between primes
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Verifying the Goldbach conjecture up to 4⋅10¹⁴
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Every odd number greater than $1$ is the sum of at most five primes
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Empirical verification of the even Goldbach conjecture and computation of prime gaps up to 4⋅10¹⁸
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A complete Vinogradov 3-primes theorem under the Riemann hypothesis
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Contextual Hidden Variables Theories and Bell's Inequalities
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Inhomogeneous Electron Gas
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An Undulatory Theory of the Mechanics of Atoms and Molecules
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A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. I
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Philosophical and mathematical reflection on Riemann's hypothesis. II The ontomathematical proof of Riemann's hypothesis in Hilbert arithmetic
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"Fundamental randomness" by the "apophatic" Kochen -Specker theorem: Toward a universal method in Hilbert arithmetic's number theory
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Primes are KS fundamentally random (but in Hilbert arithmetic, not in the standard mathematics)
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An Elementary Proof of the Prime-Number Theorem
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Generalized Poincare's Conjecture in Dimensions Greater Than Four
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Differentiable and Combinatorial Structures on Manifolds
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Stable Homeomorphisms and the Annulus Conjecture
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Deformations of Spaces of Imbeddings
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Sur la distribution des zéros de la fonction $\zeta(s)$ et ses conséquences arithmétiques
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On the distribution of primes in short intervals
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The primes contain arbitrarily long arithmetic progressions
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Primes in tuples I
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Linear equations in primes
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Bounded gaps between primes
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Small gaps between primes
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Primes in arithmetic progressions
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On the Vinogradov bound in the three primes Goldbach conjecture
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Sur la décomposition des ensembles de points en parties respectivement congruentes
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Prime Numbers in Short Intervals and a Generalized Vaughan Identity
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Zeeman-Like Topologies in Special and General Theory of Relativity
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The topology of four-dimensional manifolds
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