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Re: Re: equal distribution of last digits base ten in the primes by b-normality
*To*: mathgroup at smc.vnet.net
*Subject*: [mg52191] Re: [mg52169] Re: equal distribution of last digits base ten in the primes by b-normality
*From*: Daniel Lichtblau <danl at wolfram.com>
*Date*: Sun, 14 Nov 2004 04:30:43 -0500 (EST)
*References*: <cmve1q$sgk$1@smc.vnet.net> <200411130940.EAA01022@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Roger Bagula wrote:
> A lot of other people ( myself included)
> didn't know there was an "ancient" proof
> of this for the Prime digits either.
>
> I'm still having trouble with finding examples that aren't b-normal.
> If anybody knows of such sums and their iterators
> please let me know.
> Daniel Lichtblau wrote:
>
>>>
>>
>>I fail to see this.
>>
>>"On the random character of fundamental constant expressions" (2000) by
>>David H. Bailey and Richard E. Crandall shows that (among many other
>>things), subject to a certain hypothesis about a class of iterated map,
>>Pi is normal to base 16. Perhaps further work has been done in this area
>>since then. My very limited understanding from that article is that they
>>proved that for Pi the map does not have a finite attractor and hence
>>the second case of the hypothesis can be used.
>>
>>I do not see how the iterations above fall into that hypothesis, or how
>>one might prove there is no finite attractor.
>>
>>Daniel Lichtblau
>>Wolfram Research
I am not sure what you mean by "proof of this". If uniform distribution
of last digits (base 10) of primes, then I think that may be addressed
by the Dickson reference you rather inconveniently gave in a different post.
If you mean 10-normality of something or other, then you need to state
clearly what that something is. Such normality refers to infinite
strings of digits and it is not clear what infinite string you might
have in mind, let alone how it might be shown to be 10-normal.
Generally speaking, it would make for better posts if you carefully
define and correctly use terminology such as "b-normal", and carefully
state how you apply it or conjecture it might be applicable.
Daniel Lichtblau
Wolfram Research
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