From: numtheor@tiac.net (Bob Silverman)
Newsgroups: sci.math
Subject: Re: Reciprocals of primes
Date: Thu, 07 Nov 1996 02:19:16 GMT

gerry@mpce.mq.edu.au (Gerry Myerson) wrote:

>In article <55nd9m$ot6@news-central.tiac.net>, numtheor@tiac.net (Bob
>Silverman) wrote:
>> 
>> The period is maximal
>> iff 10 is a primitive root of p.  Generally, the length of the period is
>> the order of 10 mod p.  I don't know of any open questions. This is a 
>> completely solved problem.

>As Bob knows, the question of whether there exist infinitely many primes 
>for which the period is maximal is an open question. We "know" (in the 
>sense of the word that infuriates many regulars on this group) that 
>there are infinitely many, we even "know", asymptotically, how many 
>there are up to x, but we can't prove what we "know". 

>Gerry Myerson (gerry@mpce.mq.edu.au)

Hi Gerry,

D. Roger Heath-Brown showed that there are at most 2 exceptions, i.e. that
every a is a primitive root infinitely often with at most 2 exceptions. One
might say that the probability that 10 is one of those exceptions is rather
small.....      :-)




'You can lead a horse's ass to knowledge, but you can't make him think.'