Counting with composites Please advise

  • Context: Undergrad 
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Discussion Overview

The discussion revolves around the concept of counting composite numbers and its implications for identifying prime numbers. Participants explore whether generating all composite numbers can lead to a complete understanding of prime numbers, particularly focusing on the relationship between odd composites and missing odd primes.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions the standard for counting with composite numbers and suggests that counting odd composites could lead to identifying all primes.
  • Another participant expresses skepticism about the solvability of the problem, noting that bounding values for primes exist rather than definitive counts.
  • A participant claims to have a method for generating all composite numbers and seeks validation for the proposition that missing numbers in this context would be primes.
  • Concerns are raised about the efficiency of algorithms for handling large numbers, with one participant suggesting that the time complexity of the proposed method needs consideration.
  • Some participants discuss the potential for using known primes and Mersenne primes to test the algorithm's effectiveness.
  • There is mention of the computational challenges associated with manipulating large primes and the need for algorithms that adapt to failures.
  • One participant shares a thesis that addresses the relationship between primes and composites, while expressing doubt about the feasibility of finding large primes satisfactorily.
  • Another participant reflects on the nature of primes as both intriguing and problematic, sharing a personal anecdote about a failed attempt to generate new primes from existing ones.

Areas of Agreement / Disagreement

Participants express a mix of agreement and disagreement regarding the feasibility of the proposed methods and the relationship between composites and primes. There is no consensus on the validity of the claims made, and multiple competing views remain throughout the discussion.

Contextual Notes

Participants acknowledge limitations in their approaches, including the need for thorough testing of algorithms, the efficiency of methods for large numbers, and the inherent challenges in identifying primes based on composites.

  • #31


Have someone working with me on the code. He is pretty busy so it may take him some time to work through his stack.
 
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  • #32


If it gives you some freedom, you can try learning Python. It's picked up quickly, tutorials are available (http://docs.python.org/tutorial/introduction.html), and it has "big number" support built-in, and used seamlessly without you doing anything.
 
  • #33


Thanks for the tip
 
  • #34


Interesting thread. By range, what do you mean? a specific grouping that will be of different sizes for increasingly larger numbers , or any range from say 0 to infinity?
 

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