23298Re: A question
- Oct 1, 2011--- In firstname.lastname@example.org, "mikeoakes2" <mikeoakes2@...> wrote:
> > I can't think of a reason why any prime would be excluded from being a factor of numbers in the set.After the work Mark and Mike did, it really seems that any prime number is Euclid-style accessible. Unfortunately, I have no idea how this could be proved.
> I agree.
> > I've only gone 5 'deep', and thus far 19 is the onlyI also would understand the notion of depth in this way. When I wrote "No, I have not gone even to that depth", I actually meant I did not go to a depth at which, for instance, 11 and 17 are already shown to be Euclid-style accessible.
> > prime < 29 that hasn't shown up yet. 11 and 17 were
> > late to the party, but they eventually surfaced at depth 5.
> A is defined recursively so, rather than your "depth" (which I'm not sure I understand) I favour a measure "recursion_depth", which would enumerate the elements of A in order of their appearance as follows:-
> x*y recursion_depth
> 1 1
> 1*2 2
> 2*3 3
> 6*7 4
> 42*43 5
> 1806*13 6
> 1806*139 6
In addition to this notion of accessibility, maybe a stronger one also deserves some attention, namely the one we get when we replace "y is a prime divisor of x+1" with "y is the least prime divisor of x+1" in the definition of the set A.
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