Goldbach revisited

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• Let s make a 2 by 2 crosstabs for the number of odd pairs(P,Q) which add to 2 * N. And assume that primeness is independent of the adding to 2*N. (Which is a
Message 1 of 4 , Jan 2, 2006
Let's make a 2 by 2 crosstabs for the number of odd pairs(P,Q) which add to
2 * N.

And assume that primeness is independent of the adding to 2*N. (Which is a
separate conjecture.)

Q odd composite Q odd
prime Q odd total
P odd composite ( N - N/log(N))^2 [
N/log(N)] * [N - N/log(N) ] N * [N - N/log(n) ]

P odd prime [ N/log(N)] * [N - N/log(N) ] ( [
N/log(N)] * [N - N/log(N) ] )^2 N/log(N)

P odd total N * [N - N/log(n) ]
N/log(N) N^2

This suggests that the number of ways that primes add to 2N increases
as N increases.

Thus I propose two companion conjectures to the Goldbach conjecture.

(1) The number of ways in which an even number M is the sum of two primes
increases as M increases.

(2) The number of prime pairs that add to M is approximately what would be
expected if adding to the even number
M is independent of primeness.
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