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From: matt@oddjob.UUCP (Matt Crawford)
Newsgroups: net.math
Subject: Re: Another Prime Number Question With No Practical Application
Message-ID: <721@oddjob.UUCP>
Date: Tue, 14-May-85 22:31:30 EDT
Article-I.D.: oddjob.721
Posted: Tue May 14 22:31:30 1985
Date-Received: Thu, 16-May-85 02:05:25 EDT
References: <226@ihnet.UUCP> <574@lll-crg.ARPA> <298@faron.UUCP>
Reply-To: matt@oddjob.UUCP (Matt Crawford)
Distribution: net
Organization: U. Chicago, Astronomy & Astrophysics
Lines: 23

In article <298@faron.UUCP> bs@faron.UUCP (Robert D. Silverman) writes:

>The set is quite definitely finite. In fact it is rather small and takes
>very little computer time to generate. A better way of defining it is:
>
>The set of all primes p such that 10p + r  (r = 1,3,7,9) is also in the
>set for some r.
> 
>It is easy to convince yourself that the set should be finite based
>on probability arguments.  I don't know of a rigorous proof other
>than construction of the set.

The set YOU describe must be either empty or infinite.  Otherwise it
would have a maximum member P, but by your definition 10P+r is also
in the set.  Therefore there is no maximum member.  

Will this definition for the disputed set work?  The set consists of
{2,3,5,7} and all primes p such that int(p/10) is also in the set.
this does not make the cardinality of the set obvious, but the decision
algorithm for membership is easy.
_____________________________________________________
Matt		University	crawford@anl-mcs.arpa
Crawford	of Chicago	ihnp4!oddjob!matt