$$2 = 5-3 \\ 4 = 7-3 \\ 6 = 11-5 \\ 8 = 19-11 \\ 10 = 13-3 \\ \vdots$$
For every positive even number $n$, does there always exist a pair of prime $(p,q)$ such that $p-q =n$?
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This is similar to the Goldbach conjecture and I would expect a similar situation. I would be sure it is true but expect that there is no known proof. – Ross Millikan Nov 11 '19 at 15:29
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@RossMillikan so are Schnizel's hypothesis, hypothesis $H_n$, Bertrand's postulate, Dickson's conjecture, Polignac's conjecture, twin prime conjecture, etc. – Nov 11 '19 at 18:27
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equivalently this $$\forall m\in \mathbb{N};\exists(x,y)\in A:={(a,b):a-b=m}:$$$$2\cdot a+1,2\cdot b+1\in\mathbb{P}$$ – Nov 13 '19 at 01:27