- #31
Xevarion
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I'm pretty sure it's 0. See http://en.wikipedia.org/wiki/Prime_number_theorem#Approximations_for_the_nth_prime_number
Can This Conjecture Predict Prime Numbers?
- Context: Graduate
- Thread starter approx
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- Conjecture
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Discussion Overview
The discussion revolves around a conjecture related to predicting prime numbers through the manipulation of sets of prime numbers. Participants explore the structure of these sets and the relationships between their products and differences, examining conditions under which certain results hold true.
Discussion Character
- Exploratory
- Debate/contested
- Mathematical reasoning
Main Points Raised
- One participant introduces a conjecture involving two sets of primes, A* and B*, and proposes that if q = abs(A +/- B) is less than the square of the next prime, then q is either prime or 1.
- Another participant suggests that the problem is more complex than a previous discussion and requires different techniques to approach it.
- Some participants clarify the conjecture, proposing simplified versions and discussing the implications of the conditions set on A and B.
- There is a suggestion that every prime less than p^2 can be expressed as a difference between elements in sets A and B, where A and B are products of primes up to p.
- A later post introduces a conjecture that involves conditions on the greatest common divisor of A and B, and the relationship between primes and their factors.
- Another participant questions whether the conjecture presented is the same as their understanding, indicating potential confusion or differing interpretations of the conjecture's formulation.
Areas of Agreement / Disagreement
Participants express differing interpretations of the conjecture and its implications, indicating that there is no consensus on its formulation or the conditions under which it holds. Multiple competing views remain regarding the conjecture's validity and the methods to approach it.
Contextual Notes
Some participants note that small numbers can be checked directly, while larger numbers may require different considerations. There are also mentions of specific cases where conjectures fail, highlighting the limitations of the proposed ideas.
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