Nice grouping of primes under 105

  • Context: High School 
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    Grouping Primes
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Discussion Overview

The discussion revolves around an algorithm that generates a grouping of prime numbers under 105. Participants explore the implications of this algorithm, the nature of prime number generation, and the potential for discovering patterns or properties related to primes.

Discussion Character

  • Exploratory, Debate/contested, Conceptual clarification

Main Points Raised

  • One participant presents an algorithm that generates a grouping of primes under 105.
  • Another participant questions the purpose of the post, seeking clarification on the intent behind sharing the algorithm.
  • A participant expresses a desire to inspire others to seek algorithms that generate larger groupings of primes and aims to describe the nth prime.
  • There is skepticism regarding the feasibility of describing the nth prime, with one participant suggesting that no set of numbers can exclude the next prime number.
  • Another participant notes that the problem of generating prime numbers is known and unsolved, linking it to the Riemann Hypothesis and the lack of a single equation for generating all prime numbers.
  • A participant challenges the usefulness of the algorithm, arguing that it requires prior knowledge of prime numbers and does not utilize any inherent properties of primes.
  • In response, another participant suggests that any algorithm could be used to arrange natural numbers and identify patterns among primes, clarifying that they did not claim to find a pattern but merely commented on an interesting grouping.
  • One participant expresses skepticism about the interest in the grouping, perceiving it as a random arrangement.

Areas of Agreement / Disagreement

Participants exhibit disagreement regarding the significance and utility of the algorithm for grouping primes, with some questioning its relevance and others defending its exploratory nature. There is no consensus on the potential for generating the nth prime or the existence of a universal generating function for primes.

Contextual Notes

The discussion highlights limitations in the understanding of prime generation and the assumptions underlying the proposed algorithm. The relationship between the Riemann Hypothesis and prime generation remains unresolved.

nocat2
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The simple algorithm shown in the uploaded file generates a nice grouping of primes under 105.
 

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Is there a question there somewhere? I mean, what was your point in making this post?
 
I thought perhaps it might encourage someone to look for other algorithms that generate larger groupings. The algorithms could be described mathematically. Ultimately, my goal is to describe the nth prime!
 
nocat2 said:
Ultimately, my goal is to describe the nth prime!
I think that's a lost cause, there is no set of numbers which exclude prime number nth[next].
(Unless you decide to exclude it arbitrarily for such reasons as your computer is incapable of storing it.)
 
Last edited:
This is a known and unsolved problem in Mathematics today. Perhaps, once the Riemann Hypothesis is proven then out of it's proof will come a generating function for prime numbers. However, while we may fit selected groups of primes into some equation, there is no single equation that generates only prime numbers for any arbitrary size of primes.
 
Wait, you just arrange the numbers in some "nice" way, but you still have to know the prime numbers to fill that pattern? Where is the point? You are not using any property of prime numbers at all.
 
One could use any algorithm to arrange natural numbers, and subsequently look for identifiable patterns in resulting groups (or patterns) of primes. I did not claim to find a pattern. I only commented on a interesting group.
 
What is interesting? I just see a random arrangement.
 

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