Is There a Constant That Makes Floor[A^(3^x)] Prime for All x?

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Discussion Overview

The discussion revolves around the question of whether there exists a real number A such that the expression Floor[A^(3^x)] yields a prime number for all values of x. The inquiry touches on theoretical aspects of number theory and the properties of prime numbers.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions the validity of the premise, suggesting it does not make sense.
  • Another participant proposes the possibility of Mills' constant being relevant to the discussion.
  • A subsequent reply confirms that Mills' constant is indeed the concept being referenced.
  • A link to a Wikipedia page about Mills' constant is provided for further exploration.

Areas of Agreement / Disagreement

Participants express differing views on the initial premise, with some finding it nonsensical while others suggest a connection to Mills' constant. The discussion does not reach a consensus on the validity of the original question.

Contextual Notes

The discussion lacks detailed exploration of the mathematical implications of Mills' constant and its relationship to the original question. Assumptions about the nature of primes and the behavior of the Floor function are not fully articulated.

Dragonfall
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I think I read this somewhere, but I'm not sure it's right: is there a real number A such that Floor[A^(3^x)] is prime for all x?
 
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That doesn't make any sense.
 
Are you thinking perhaps of Mills' constant?
 
Mill's constant! That's the one.
 

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