# MATH: Goldbach Conjecture

John K Clark (johnkc@well.com)
Thu, 2 Jan 1997 21:22:42 -0800 (PST)

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On Thu, 02 Jan 1997 Alexander Chislenko <alexc@firefly.net> Wrote:

>I tried to estimate the chances that it [Goldbach Conjecture]
>can be disproven assuming random distribution of primes.

Primes are not distributed randomly, they become rarer as integers get bigger.
The number of primes less than integer X is approximately equal to X/logX ,
the larger the X the better the approximation.

>The chances, after a certain [low] threshold N, are
>virtually nil. [...] is it such a big deal to have a
>mathematical "fact" that is not *exactly* proven, but is
>certain to 99.9999999999999999999999% ?

I am flying to New York City for the first time. I know absolutely nothing
about the city except that 7 million people live there. The first person I
see when I get off the airplane is a woman. I conclude that there is a
99.9999999999999999999999% chance that everyone in New York City is a woman.

The situation is FAR worse when you talk about prime numbers, we have a
ridiculously tiny sample to work with, we have only found a few trillion
prime numbers and there are an INFINITE number of them.

John K Clark johnkc@well.com

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