Should Goldbach's Conjecture be restated thus? *Every integer $>3$ can be expressed as the average of two primes.*

Question

Yes, every, not just even.

If a number is the average (or difference) of two primes, by doubling the number it has a partition of those two primes. So, for example, $(7+31)/2=19$ becomes $7+31=2*19=38$.

Since every $n*2$ is even, GC has an underappreciated claim upon every odd n > 3 (including every prime). No other conjecture is required.

CSV of first 100,000: int, diff, p1, p2, type