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MathGroup Archive 2004

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Re: equal distribution of last digits base ten in the primes by b-normality

  • To: mathgroup at smc.vnet.net
  • Subject: [mg52157] Re: equal distribution of last digits base ten in the primes by b-normality
  • From: Bill Rowe <readnewsciv at earthlink.net>
  • Date: Fri, 12 Nov 2004 02:14:33 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

On 11/11/04 at 4:52 AM, tftn at earthlink.net (Roger Bagula) wrote:

>The {1,3,7,9} last digits of the primes modulo 10 equal
>distribution conjecture has never been proved, but I have a b-
>normal iteration for it.. What that says is that the modulo ten
>function is equally spaced over the base ten. This is the same
>argument that Dr. Bailey used to say that the digits of Pi are
>equally probable over base 16 using his Pi digits formula. Thus if
>Bailey's proof is acceptable so is this. 

There are a variety of algorithms for computing the nth digit of Pi. Given a suitable algorithm, there is the possibility of devising a strict mathematical argument showing the digits of Pi are equally probable base 16. I will assume this is what Bailey did.

But this argument will not hold for primes modulo 10. The reason is there is no algorithm for computing the nth prime. All that can be done is gather empirical evidence in support of the hypothesis. This is quite different from a rigourous mathematical argument about the digits of Pi base 16.

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