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kingtaf
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Prove or disprove: If n is an integer and n > 2, then there exists a prime p such that
n < p < n!.
n < p < n!.
Prime Factorial Proof: Existence of a Prime Between n and n!
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Discussion Overview
The discussion centers around the existence of a prime number p such that n < p < n! for integers n greater than 2. Participants explore various approaches to prove or disprove this statement, including references to Bertrand's postulate and the prime factors of n! - 1.
Discussion Character
- Exploratory, Debate/contested, Mathematical reasoning
Main Points Raised
- One participant proposes the existence of a prime p between n and n! for n > 2 and invites proof or disproof.
- Another suggests considering the prime factors of n! - 1 as a potential proof method.
- Several participants reference Bertrand's postulate, with mixed feelings about its complexity in relation to the problem.
- A participant describes a specific example using 5! to illustrate how the prime factors of n! - 1 relate to primes greater than n.
- Another participant questions whether there are prime factors of n! - 1 that are less than n.
- A later reply expresses satisfaction with the understanding gained from the discussion, indicating a resolution for that participant.
Areas of Agreement / Disagreement
There is no clear consensus on the proof or disproof of the statement. Multiple competing views and approaches remain, with some participants finding clarity while others express ongoing confusion.
Contextual Notes
Participants mention the complexity of applying Bertrand's postulate and the potential for simpler proofs involving n! - 1, but do not resolve these complexities or assumptions.