Explicit upper bound for r0(n)

Numerical computations seem to show that r_{0}(n) is always less than 0.07\log^{4} n whenever n>28. Solving the equation x=0.07\log^{4} x, one gets as a threshold the value x0\approx 0.25216..., hence every even integer greater than 3 is the sum of two primes, as the small cases (less than 57) can be easily checked by hand.