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## theorems

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• What theorems/proofs exist of the form: If a
Message 1 of 2 , Dec 18, 2005
What theorems/proofs exist of the form:

If a<x<b, then there are at least z-many primes?

I'm familiar with Bertrand's postulate, where:
b=2a and z=1

(a more formal definition is here:
http://mathworld.wolfram.com/BertrandsPostulate.html )

What others are there? I'll look into this myself... but in the
meantime many people on this list might already have these tidbits
memorized... :)

Regards,
Jeremy
• As a fun little exercise I wrote an algorithm that will give a minimum bound for pi(p(i)^2). I wish I could turn at least part of it into some sort of proof.
Message 2 of 2 , Dec 26, 2005
As a fun little exercise I wrote an algorithm that will give a
minimum bound for pi(p(i)^2).

I wish I could turn at least part of it into some sort of proof.
(For example, for all i>12, can it be proved that there are at least
X many primes between p(i)^2 and p(i)?) But I'm not skilled at
proofs, so the paper only highlights an algorithm.

(Is there such a proof out there with that form, by the way? I tried
to ask about that earlier, but I think my email got drowned in a
flurry of other posts. Or maybe I asked the question poorly.)

It's probably nothing significant... just a little trinket. But I
wrote it up as I explored it if anyone wants some light reading:
http://homepage.mac.com/bricolage1/primes/PatternsPSquared.pdf

Hope everyone who's on holiday is having a pleasant and safe time.
Regards,
- Jeremy
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