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Topic: PNT look-alikes
Replies: 15   Last Post: May 19, 2011 2:45 AM

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Posts: 2,394
Registered: 8/3/07
Re: PNT look-alikes
Posted: May 18, 2011 2:24 PM
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On May 18, 11:16 am, Transfer Principle <> wrote:
> By Fermat's Little Theorem (Carmichael generalization), the number
> of digits after which 1/m repeats must divide lambda(m), which in
> turn divides phi(m). It follows that if m is "decimal-maximal" (or
> "base-b-maximal to any base b), it must be _prime_.

OK, I found a few more relevant Wikipedia pages:

First, the elements of M are called "full reptend primes":

Sequence A001913 in Sloane's OEIS gives the sequence.

> Related question: what is rho(M,P) (Katz notation), the density of
> M _in_P_? I don't know the answer to this one.

The Wikipedia page gives that the conjectured value of rho(M,P) is
something called "Artin's constant," C_Artin = 0.3739558136...

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