I'm new to proofs, does anybody have a proof that three times a prime is always greater than the next consecutive prime?

Asked Mar 11 '23 at 10:12

Active Mar 11 '23 at 10:12

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Numbering the primes in the fashion {|P₁ -> 2 | P₂ -> 5 | P₃ -> 7 | P₄ -> 11 | ... |},

Can I prove that 3P_n > P_n+1? My gut is kind of telling me it's true, but I'm not really sure how to go about proving (or disproving) it without knowing something to do with the maximum gaps between primes, or something like that?

asked Mar 11 '23 at 10:12

Ozymandias

5

Look up Bertrand's postulate, which is stronger than you need. – Patrick Stevens Mar 11 '23 at 10:17
@PatrickStevens It could be interesting to see whether this problem is significantly easier to prove, though. – Arthur Mar 11 '23 at 11:57

I'm new to proofs, does anybody have a proof that three times a prime is always greater than the next consecutive prime?

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