[QUOTE=davar55;245530]Our key
difference is my claims based on my conjecture (1), that the ratio is in
fact bounded above, which denies the fundamental assumption of the
current conjecture, namely that the distribution of primes can be "modeled"
as a random (poisson or otherwise) process. They can not, except as an
approximation. The primes, just as the integers, are immutable, not random.[/QUOTE]

So I suppose you believe that prime gaps are bounded above as well?

[TEX]{q_n}=2^{e^{-\gamma}}^n \gt 1[/TEX] ? that's what i got out of it.

[QUOTE=science_man_88;245582][TEX]{q_n}=2^{e^{-\gamma}}^n \gt 1[/TEX] ? that's what i got out of it.[/QUOTE]

Go back and do it again, then.

[QUOTE=CRGreathouse;245587]Go back and do it again, then.[/QUOTE]

[url]http://upload.wikimedia.org/math/2/a/b/2ab375e3e6dfcefc066d1eb3c9172fe1.png[/url] is what I can see it relating to on that page, that raised to the power of nis my best guess though I'm unsure of a symbol in the image so I'm unclear on what it could mean.

[QUOTE=science_man_88;245599][url]http://upload.wikimedia.org/math/2/a/b/2ab375e3e6dfcefc066d1eb3c9172fe1.png[/url] is what I can see it relating to on that page, that raised to the power of nis my best guess though I'm unsure of a symbol in the image so I'm unclear on what it could mean.[/QUOTE]

The image you linked to is a property of the function. The definition is given in the first (short!) paragraph.

[QUOTE=CRGreathouse;245601]The image you linked to is a property of the function. The definition is given in the first (short!) paragraph.[/QUOTE]

then I'm clueless because all i get with reading that first paragraph is that [TEX]2^{e^-{\gamma}} + o(1)[/TEX] grows faster than [TEX]\sqrt[n] q_n[/TEX] in which case unless it's an upper bound they should intersect in my mind.

[QUOTE=science_man_88;245603]then I'm clueless because all i get with reading that first paragraph is that [TEX]2^{e^-{\gamma}} + o(1)[/TEX] grows faster than [TEX]\sqrt[n] q_n[/TEX] in which case unless it's an upper bound they should intersect in my mind.[/QUOTE]

Rewrite the equation I have until it's in the form in the definition ("foo = o(bar)"), then substitute the appropriate functions into the definition. What do you get?

[TEX]{\sqrt[n]{q_n}} - {2^{e^{-\gamma}}}\lt 1[/TEX] ?

[QUOTE=science_man_88;245619][TEX]{\sqrt[n]{q_n}} - {2^{e^{-\gamma}}}\lt 1[/TEX] ?[/QUOTE]

Where do you even see a "<"? Clearly you're not using the definition (or, rather, you're not using either of the definitions).

[QUOTE=CRGreathouse;245624]Where do you even see a "<"? Clearly you're not using the definition (or, rather, you're not using either of the definitions).[/QUOTE]

I don't see how to do grows faster than and that's my understanding from what I read.

[QUOTE=CRGreathouse;245575]So I suppose you believe that prime gaps are bounded above as well?[/QUOTE]

No, two different issues.

Prime gaps (differences) are known to increase without an absolute upper bound.

In the MPE case, it's the ratio of consecutive terms I claim is bounded,
not the differences.