Has the Prime Number Distribution Puzzle Been Cracked?

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Discussion Overview

The discussion revolves around the conjecture regarding the distribution of prime numbers, specifically whether every prime can be generated through a specific algorithm involving the partitioning of primes into two sets. Participants explore various mathematical approaches and theories related to prime number generation and distribution.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant presents a conjecture involving the creation of two numbers, A and B, from the first (n-1) primes, suggesting that all primes can be generated through this method under certain conditions.
  • Another participant questions the exhaustiveness of the prime sets generated, noting that there are infinite exponent sets that could yield results within the allowed range.
  • Some participants discuss the limitations of polynomial functions in generating primes, stating that no nonconstant polynomial can yield only prime numbers for all integer inputs.
  • There is a contention about the existence of functions that can generate primes, with some arguing that while certain functions can yield primes, they do not do so exclusively.
  • Several participants engage in a debate about the implications of known theorems regarding prime distributions, including references to the Riemann hypothesis and the prime counting function.

Areas of Agreement / Disagreement

Participants express differing views on the conjecture regarding prime generation, with some supporting the proposed method while others challenge its validity. There is also disagreement on the nature of functions that can generate primes, with some asserting that no such function exists, while others argue that certain functions can yield primes under specific conditions. The discussion remains unresolved.

Contextual Notes

Participants note various mathematical assumptions and limitations, such as the dependency on the choice of exponents and the scope of polynomial functions. The discussion highlights the complexity of prime number theory and the challenges in proving conjectures related to prime distributions.

  • #31
Why have the last two posts started:

Originally posted by HallsofIvy

and then contained nothing posted by me?
 
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  • #32
Originally posted by HallsofIvy

Because i like short threads. Best wishes: Erik-Olof or Sariaht
 
  • #33
Should I feel flattered?
 
  • #34
How am I supposed to feel, corrected?
 

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