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I will argue that $i$ can not have tween primes when: $i=6+5⋅z+(7+6⋅z)y$ or $i=4+5⋅z+(5+6⋅z)y$ or $i=8+7⋅z+(7+6⋅z)y$ or $i=6+7⋅z+(5+6⋅z)y$ Where $z≥0$ or $y≥0$ (integers) The tables are written with {matrix}, but intended just to be tables. I will start with the following table. $$\begin{matrix...