Re: prime number

To: CALC-TI@LISTS.PPP.TI.COM
Subject: Re: prime number
From: Polonio <polonio_@YAHOO.COM>
Date: Fri, 22 May 1998 00:02:21 +0200
Organization: Telefonica Transmision de Datos
References: <01bd7de9$e53a5820$0100007f@localhost> <355C8458.7FB445BA@erols.com>
Reply-To: Polonio <polonio_@YAHOO.COM>
Xref: paladin.american.edu bit.listserv.calc-ti:23049

>Rhombus wrote:
>
>>  Take any prime number P.What is the probability that P-1 is divisible
>> by 6 ?Is the answer really 1/2 ?  Jan Vermeylen

Yes, I think the probability is exactly 1/2.

I will try to explain why.

If you take any prime numer bigger than 3 it will be an odd number, and not
divisible by three. Threfore, P-1 is an even number. Then, the question is
just the same as

"What is the probability that P-1 is divisible by 3?"

If you take three consecutive numbers (P, P-1, P+1), one and just one is
divisible by three. We already know that P is not divisible by three. Then,
or P-1 is divisible by 3 or P+1 is divisible by three. It seems very clear
that the probability of being P-1 divisible by three is 1/2.

I know that this is not a real demostration, but I think it is clear enoght.
Anyway, you can make a little program in your computer (or in your calc) and
prove it, I am sure the afirmation will show true.

Polonio

References:

prime number

From: Rhombus <math@rhombus.be>

Re: prime number

From: Tim Brierley <Brierley@EROLS.COM>

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