Efficient Prime Number Algorithm: Seeking Feedback and Offering Unique Insights

[MechaMiles]

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.

 

[Amir Livne]

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?

 

[MechaMiles]

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.

 

[Amir Livne]

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.

 

[blue_raver22]

First of all, I would like to commend you for your efforts in developing this prime-seeking algorithm and for seeking feedback from the community. I understand the importance of continuously improving and refining our methods and techniques, and seeking feedback is a crucial step in this process.

I have taken a look at your thesis and I must say, your approach to partitioning the set of naturals between prime and composites is indeed unique and interesting. Your rigorous structural schema provides a clear and systematic way of understanding the distribution of prime numbers and can potentially lead to further insights in this area.

However, I do agree that the efficiency of the algorithm is a critical aspect to consider. While it may not be computationally better than existing algorithms, the unique insights it offers can still be valuable in advancing our understanding of prime numbers. Perhaps exploring ways to improve the efficiency of the algorithm while still maintaining its structural integrity could be a potential avenue for future research.

In addition, I also suggest reaching out to other experts in the field and presenting your algorithm at conferences or workshops to gather more feedback and potentially collaborate on further developments. Overall, I believe your algorithm has the potential to contribute to the ongoing research on prime numbers and I look forward to seeing its further development. Best of luck in your endeavors.