--- In primenumbers@y..., Nathan Russell <nrussell@a...> wrote:

> >-The prime number theorem would explain a factor of maybe a

> > little over 1 - not 1.5, and DEFINATELY not 60

>

> Correction - we're talking about a high power of the natural log,

> not the log itself. As such, the increase would be quite likely

> over 2 but still not 60.

I think that you are missing a big piece of the equation --

forget about prime numbers for a minute. How many 5-row triangles

in positive odd integers are there, where the maximum sum is 2175?

Call that number T(5). Then, how many 6-row triangles in positive

odd integers are there, where the maximum sum is 9069? Call that

number T(6).

The ratio T(6)/T(5) is at least 60, probably more. I don't have a

clue to its exact value, but it's not too difficult to see that

the "average" 5-row triangle with sum <= 2175 can be extended

to a 6-row triangle with sum <= 9069 in at least 60 ways.