# 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.

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