Published July 28, 2025 | Version v1
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A Generating Function Framework for Goldbach's Conjecture: Visual Symmetry and Probabilistic Modeling

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This paper offers a heuristic and visual approach to Goldbach’s Conjecture, focusing on intuitive representations and structural patterns among prime numbers. Departing from traditional proofs, it presents conceptual tools and illustrative diagrams that aim to inspire deeper exploration of this unsolved problem in number theory. It is intended for both enthusiasts and researchers seeking fresh perspectives.

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Dates

Issued
2025-07-28

References

  • @article{hardy_littlewood_goldbach, author = {Hardy, G. H. and Littlewood, J. E.}, title = {Some problems of 'Partitio Numerorum': III. On the expression of a number as a sum of primes}, journal = {Acta Mathematica}, year = {1923}, volume = {44}, pages = {1--70}
  • @book{cramer_primes, author = {Cramér, Harald}, title = {On the Order of Magnitude of the Difference Between Consecutive Prime Numbers}, publisher = {Mathematica Scandinavica}, year = {1936}
  • @article{maynard_gaps, author = {Maynard, James}, title = {Small gaps between primes}, journal = {Annals of Mathematics}, year = {2015}, volume = {181}, number = {1}, pages = {383--413}