Fw: prime number
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Fw: prime number
>Hi Jan,
>
>At 23:06 12.05.1998 +0200, you 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
>
>Suppose that a and d are natural numbers s.t. gcd(a,d)=1 and let
>
> pi SUB [d,a](x) = # {primes <=x s.t. p = a mod d}
>
>and
>
> pi(x) = # {primes <=x}
>
>for any real number x > 0. According to a celebrated theorem by de la
Vallée
>Poussin the following holds
>
> lim (pi SUB [d,a](x)/ pi(x), x, inf) = 1/euler_phi(d)
>
>Setting a=1 and d=6 you get for that probability
>
> 1/euler_ph(6) = 1/2,
>
>that is your guess was correct.
>
>Cheers,
>
>Johann
>
>___________________________________________________________________
>
>Johann Wiesenbauer,
>Institut f. Algebra und Diskrete Mathematik
>der Technischen Universitaet Wien
>Wiedner Hauptstrasse 8-10,
>A1040-Vienna, Austria
>
>Tel.: +43 1 58801 5462
>Fax: +43 1 5815335
>
>