Density of primes between square numbers

1. May 14, 2009

Loren Booda

Is the density of primes considerably greater nearer the geometric average of two consecutive square numbers?

[Think of deconstructing a square of integral area n2 into composite rectangles of diverging (n-1)(n+1), (n-2)(n+2), (n-3)(n+3)... .]

This reasoning may work to a lesser yet significant degree with powers greater than two.

2. May 14, 2009

Hurkyl

Staff Emeritus
I'm boggled as to why you would say "the geometric average of two consecutive square numbers" rather than "the product of two consecutive numbers".

Unless you stick to very small numbers, I can see no reason why the answer to your question would be "yes". What would suggest it?

I can't make any sense out of the rest of your post. I mean that literally: not a judgement of right or wrong, but as a judgement of whether or not I can extract meaning from that sequence of words and symbols.

3. May 14, 2009

Loren Booda

Thank you for being understanding, Hurkyl. Mine is a half-baked idea.

4. May 15, 2009

CRGreathouse

How near?

I'm almost sure this isn't true unless taken to the trivial extreme that n(n+1) is itself composite for n > 1.

5. May 15, 2009

Loren Booda

CR,

I appreciate your input. I should look before I lemma.

6. May 15, 2009

CRGreathouse

Loren: I didn't see your other post (#3) before I posted -- sorry. I wouldn't have posted otherwise.