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4

I am interested in the following question:

Is it known that $2$ is a primitive root modulo $p$ for infinitely many primes $p$?

there is some information about Artin's conjecture in http://en.wikipedia.org/wiki/Artin%27s_conjecture_on_primitive_roots

I need to know if it is up to date and if one can say something about the case n=2.

edited Dec 2 2010 at 8:56

Andrey Rekalo
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asked Dec 2 2010 at 1:18

Kate Juschenko
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No. $\!\!\!\!\!$ – David Hansen Dec 2 2010 at 1:25

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@David: there were two questions. @Kate: Pieter Moree at Bonn will know the most recent advances if there were any. – Franz Lemmermeyer Dec 2 2010 at 9:00

@Franz: Thanks for the information – Kate Juschenko Dec 2 2010 at 19:28

S. Carnahan · Answer 1 · 2010-12-02 08:30:26Z UTC

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I'm not an expert, but the content of this article (last modified December 2004) suggests the Wikipedia article is reasonably up-to-date.

answered Dec 2 2010 at 8:30

S. Carnahan♦
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Bugs Bunny · Answer 2 · 2010-12-02 09:37:11Z UTC

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It follows from GRH. Not known on its own.

answered Dec 2 2010 at 9:37

Bugs Bunny
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yes, the citations to this result are included here: en.wikipedia.org/wiki/… – Kate Juschenko Dec 2 2010 at 19:24

Artin’s conjecture for n=2

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