Efficient Prime Number Algorithm: Seeking Feedback and Offering Unique Insights

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Discussion Overview

The discussion centers around a proposed algorithm for identifying prime numbers, which the author claims offers unique insights despite not being computationally superior to existing methods. The conversation explores the algorithm's structure, its theoretical implications, and its relationship to number theory and algebraic geometry.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • The author presents a prime-seeking algorithm based on a structural schema that partitions natural numbers into primes and composites.
  • One participant notes that any odd composite number can be expressed as a sum of consecutive integers of length less than √N, which they found to be an interesting property not covered in their studies.
  • Another participant questions the efficiency of the algorithm, suggesting that testing all bases from 1 to N/3 to find sequences summing to N may not be optimal.
  • The author acknowledges the algorithm's inefficiency but emphasizes its goal of stimulating new perspectives in natural number theory through geometric interpretations.
  • A participant mentions the relevance of algebraic geometry in modern number theory, contrasting it with the author's approach while expressing hope for potential insights.
  • One participant appreciates the author's use of Hebrew variables in the paper, indicating a positive reception of the stylistic choice.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and appreciation for the proposed algorithm, with some acknowledging its unique insights while others critique its efficiency. There is no consensus on the algorithm's effectiveness or its implications for number theory.

Contextual Notes

The discussion highlights limitations in the algorithm's efficiency and the need for a comprehensive understanding of the author's thesis to fully grasp the proposed ideas. There are also references to existing theories and approaches that may not align with the author's perspective.

Who May Find This Useful

Readers interested in number theory, algorithms for prime identification, and the intersection of geometry and mathematics may find this discussion relevant.

MechaMiles
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I would really like to get some constructive feed back on this prime-seeking algorithm. Computationally it's no better than the rest. However, it does offer some unique insight.
I have partitioned the set of naturals between prime and composites using a rigorous structural schema that I prove in the following thesis:

https://sites.google.com/site/primenumbertheory/home/the-prime-thesis

Let me know what you think. I appreciate any further insight the community can offer me.
Shalom.
 
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The article is quite long, so I skipped a few parts.

If I understand correctly, your observation is that any odd composite number N is a sum of a series of consequtive integers of length < √N. This is a nice property, I for one didn't know it, and it wasn't covered in my number theory course.

But I don't understand what the algorithm is. From what I could gather, you test all the bases for the sequence, from 1 up to N/3, and check if they start a sequence that sums up to N.
This doesn't seem very efficient. Is this what you meant?
 
You have understood the primitive algorithm. You're right, it's not efficient. However, it is generalized as the thesis develops and removes all impossible values in the set of test subjects (you have to read the whole paper to understand this). Still, the fully developed algorithm is not all that efficient as a prime tester. The idea, however, is not to render a computationally efficient prime test so much as to stimulate and promote the idea that if natural number theory could be placed on some geometric palette, the key to primes might unfold.
 
I believe number theory involves a great deal of algebraic geometry nowadays. It's not at all like the approach in your paper, but if this leads to something, it'll be wonderful.
Even if you don't prove new theorems, elementary proofs of existing theorems are ofter enlightening.

PS. I liked your use of Hebrew variables in the paper. Nice touch.
 

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