  Some interesting chaos phenomena have been found in the difference of prime
numbers. Here we discuss a theme about the sum of two prime numbers, Goldbach
conjecture. This conjecture states that any even number could be expressed as
the sum of two prime numbers. Goldbach partition r(n) is the number of
representations of an even number n as the sum of two primes. This paper
analyzes the statistics of series r(n) (n=4,6,8,...). The familiar 3 period
oscillations in histogram of difference of consecutive primes appear in r(n).We
also find r(n) series could be divided into different levels period oscillation
series. The series in the same or different levels are all very similar, which
presents the obvious fractal phenomenon. Moreover, symmetry between the
statistics figure of sum and difference of two prime numbers are also
described. We find the estimate of Hardy-Littlewood could precisely depict
these phenomena. A rough analyzing for periodic behavior of r(n) is given by
symbolic dynamics theory at last.
