# Re: Primes and Probability

From: Lee Corbin (lcorbin@ricochet.net)
Date: Sat May 12 2001 - 20:57:02 MDT

Spike writes
>> Now I would think that surely the probability that C+2 is
>> prime is indeed proportional to 1/ln(C+2). Yes? It would be
>> marvelous if someone had found otherwise. What's the connection?

>Since we have no reason to believe that the probability of C+2
>is anything other than 1 / ln(C+2), lets assume it so. Now open
>primes (neither of which can be 2), multiply them together to
>generate the composite C. Now fill down, C+2, C+4, and so on.
>In the next column calculate 1 / ln {the first column}. The second
>column is the probability of each number to its left being prime.
>Now calculate the cumulative probability of C+2 and C+4 prime,
>then C+6 also prime, and so on.
>
>What did you find out?

All I know is (1) one of C+2, C+4, C+6 is composite, so summing
the probability is going to start giving a funny result, (2) 1/lnx
is a rather poor approximation, and so summing it is doubly suspicious.

But I have some good materials on "The Prime Number Theorem" and
will try to have a go at them.

Lee

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