Compilations of proofs of Euclid's Theorem on primes

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Discussion Overview

The discussion revolves around the search for references and compilations of proofs related to Euclid's Theorem on the infinitude of primes. Participants express interest in both existing compilations and new approaches to demonstrating the theorem.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant requests references for compilations of proofs of Euclid's Theorem, specifically seeking alternatives to the works of Paulo Ribenboim.
  • Another participant mentions a compilation of 183 proofs found on Wikipedia, suggesting it as a resource.
  • A third participant expresses gratitude for the mention of Arxiv but indicates that describing the proofs in detail may be impractical due to their number.
  • A later reply introduces a new article by a participant presenting three new demonstrations of the infinitude of primes, including a reformulation of Euclid's proof using geometric concepts involving angles between vectors in higher dimensions.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best resources for proofs, and multiple viewpoints regarding the availability and presentation of proofs remain. The introduction of new demonstrations adds further complexity to the discussion.

Contextual Notes

Some limitations include the potential for missing assumptions in the new proofs and the dependence on specific mathematical definitions related to the geometric approach discussed.

DaTario
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TL;DR
Hi All. Does anybody have a reference (besides those of Paulo Ribenboim) where one can find a compilation of demonstrations of the Euclid's theorem on the infinitude of primes?
Hi All. Does anybody have a reference, (book, internet site) - besides those books of Paulo Ribenboim - where one can find a compilation of demonstrations of the Euclid's theorem on the infinitude of primes?
As a suggestion, if the known proofs are neither too many not too long, it would be nice to have them described here in this post.
DaTario
 
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Thank you, mfb, very much. I have forgotten the Arxiv.
Let's forget about describing them here...too many.
 
Last edited:
News in this topic. I ended up publishing an article in the meanwhile where I present three new demonstrations of the infinitude of prime numbers. One is actually a new formulation of the proof given by Euclid expressed in terms of angles between vectors of an entire lattice in k dimensions. Although this is geometry in k dimensions, it is only necessary in this proof to use the dot product between pairs of vectors to check orthogonality. Below is the link to the article.

https://ems.press/journals/em/articles/17433

https://www.researchgate.net/publication/348610736_Infinitude_of_primes_Euclid's_proof_using_angles_between_lattice_vectors

Best wishes.
 

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