My interpretation is that the ratio column is approaching 0, with unusual rapidity for this sort of problem, so in the long run no $ \log \log$ terms. Note that, for any prime not printed, the final column must be even closer to 0 than nearby primes that are printed.
The bad news
In short, if $R(p)$ is that I do not see how the number of primes up to complete Ramanujan's construction as in "superior highly composite numbers," as his recipe gives factorizations for world champion numbers, and her we $p-2$ that are stuck with primes. Maybe something can be done with factors of quadratic residues $p-1$ or \pmod p,$ and if $p+1$ but N(p)$ is the number of primes up to $p-2$ that are quadratic nonresidues $\pmod p,$ I suggest
$$ \lim_{p \rightarrow \infty} \frac{R(p) \log p}{p} = \lim_{p \rightarrow \infty} \frac{N(p) \log p}{p} = \frac{1}{2}. $$
From David's comment, this is also the prediction of a wild guesscertain generalized Riemann Hypothesis.
p res non diff diff/(res + non) 56039 2744 2941 -197 -0.0346526 56333 2936 2775 161 0.0281912 59399 2902 3102 -200 -0.0333111 61333 2976 3193 -217 -0.0351759 65539 3354 3189 165 0.0252178 69833 3351 3571 -220 -0.0317827 71971 3652 3471 181 0.0254106 81197 4074 3872 202 0.0254216 85223 4038 4259 -221 -0.0266361 85669 4053 4285 -232 -0.0278244 88919 4188 4425 -237 -0.0275165 89591 4216 4458 -242 -0.0278995 89659 4454 4229 225 0.0259127 95989 4504 4747 -243 -0.0262674 p res non diff diff/(res + non)
