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I define Goldbach counting function with N > 0 and square-free P > 0.Decomposition of this function is discovered and deduction formula is found. Ipropose a hypothesis on upper bound of Goldbach counting function and provethat Goldbach conjecture is true under this hypothesis. Also, I propose asecond hypothesis on upper bound of Goldbach counting function and prove thatthe twin prime conjecture is true under this hypothesis

A Hypothesis on Upper Bound of Goldbach Counting Function