Compilations of proofs of Euclid's Theorem on primes

In summary, the conversation discusses the search for a compilation of demonstrations of Euclid's theorem on the infinitude of primes, with a suggestion to include them in a post. The conversation also mentions a new article published on the topic, which presents three new demonstrations of the theorem using geometry in k dimensions. Links to the article and related research are provided.
  • #1
DaTario
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TL;DR Summary
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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  • #3
Thank you, mfb, very much. I have forgotten the Arxiv.
Let's forget about describing them here...too many.
 
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  • #4
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.
 

FAQ: Compilations of proofs of Euclid's Theorem on primes

1. What is Euclid's Theorem on primes?

Euclid's Theorem on primes states that there are infinitely many prime numbers. In other words, there is no largest prime number and the list of prime numbers goes on forever.

2. Why is Euclid's Theorem on primes important?

Euclid's Theorem on primes is important because it is one of the oldest and most fundamental theorems in mathematics. It has been proven and studied for over 2,000 years and has many important applications in number theory, cryptography, and other areas of mathematics.

3. How did Euclid prove his theorem on primes?

Euclid's proof of his theorem on primes is known as the "Euclidean proof" and it uses a proof by contradiction method. He assumed that there was a largest prime number and then showed that this assumption led to a contradiction, thus proving that there is no largest prime number.

4. Are there any other proofs of Euclid's Theorem on primes?

Yes, there are many other proofs of Euclid's Theorem on primes. Some of these proofs use different methods and techniques, such as algebraic and analytic methods. However, the Euclidean proof remains the most well-known and widely studied.

5. Can Euclid's Theorem on primes be applied to other types of numbers?

Yes, Euclid's Theorem on primes can be applied to other types of numbers, such as rational and complex numbers. However, the theorem only holds true for positive integers, as prime numbers are defined as positive integers with exactly two distinct divisors.

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