## Re: [PrimeNumbers] Re: Yet another factoring puzzle

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• ... But is that more or less remarkable than the expectation of any one of Phil Taylor s darts landing in the region around where it actually landed? You only
Message 1 of 23 , Sep 25 3:08 PM
> > Exercise 6: Find the complete factorization of F(n) for at
> > least one even integer n > 600.
> As far as I can tell, no-one (apart from the setter)
> yet solved Exercise 6, which can be done in less
> than 2 minutes, using OpenPFGW. What is remarkable
> quickly. Heuristically, that was not to be expected.

But is that more or less remarkable than the expectation of
any one of Phil Taylor's darts landing in the region around
where it actually landed? You only chose that target after
the arrow had landed, I'm sure.

How many mathematical diversions have you looked at
via the medium of numerical computation? How many of
them would you expect to be remarkably easier than
expected to solve? Probably a non-zero answer. Don't
be surprised that one particular example was one.

Knowing what he's trying to say, even if he's not getting
it across clearly,
Phil
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• ... It happened thus: 1) I determined to factorize F(n)=((n^2-9)/4)^2-5 for n
Message 2 of 23 , Sep 27 2:52 PM

> You only chose that target after
> the arrow had landed, I'm sure.

It happened thus:

1) I determined to factorize F(n)=((n^2-9)/4)^2-5 for
n <= 300, completely. As later shown in "factordb", I succeeded.

2) Meanwhile I ran OpenPFGW on n in [301,600], hoping for a
quick outlier and found none.

3) I estimated the probability of an easily discoverable
completely factorization for n>600 and found it to be small.

4) Recalling how I had once been caught out before by
a "probably no more" heuristic, I set a lone process running on
n in [601, 10000]  so as not to be caught out again by Jens.

5) When I later looked  and pfgw.log, it had found a hit at
n=608.

So yes, Phil, you are quite correct that the puzzle was set
after this finding. However the heuristic that I gave was
made prior to my discovery, else I would not have said that
I was surprised.

The point that you are making (I think) is that I do such
expsriments often and only notice when the result is unexpected.
I don't tell folk about all the boring times when a negative
heuristic is borne out by a null result. That is the selection

effect.

David (guilty of not boring folk with what is routine)

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