
Re: PNT lookalikes
Posted:
May 18, 2011 2:24 PM


On May 18, 11:16 am, Transfer Principle <lwal...@lausd.net> 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 "decimalmaximal" (or > "basebmaximal to any base b), it must be _prime_. > http://en.wikipedia.org/wiki/Repeating_decimal > http://en.wikipedia.org/wiki/Carmichael_function
OK, I found a few more relevant Wikipedia pages:
First, the elements of M are called "full reptend primes":
http://en.wikipedia.org/wiki/Full_reptend_prime
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...
http://en.wikipedia.org/wiki/Artin%27s_conjecture_on_primitive_roots

