9070Re: primes, differences, a hastily constructed puzzle :-) !
- Oct 4, 2002--- In primenumbers@y..., Nathan Russell <nrussell@a...> wrote:
> >-The prime number theorem would explain a factor of maybe aI think that you are missing a big piece of the equation --
> > 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.
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
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.
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