The following question grows out of my thinking about the distribution of primes and twin primes. I could provide a lot of background as to how I arrived at this question, but that background isn't necessary to understand or solve the question. I can't provide any substantive work on the question itself because I am at an impasse. However, there might be some keener or more knowledgable minds out there that can provide some insight, so I'll ask.
The question concerns the number of distinct prime factors in products of members of a certain set. The factorial function looks at products of all positive integers up to a certain value, and the primorial function looks at products of prime numbers only up to a certain value. The set I am interested in is the ordered set $S=\{s|s=6k\pm 1, k \in \mathbb Z_+\}$, i.e. $S=\{5,7,11,13,\dots\}$. $S$ contains all of the primes greater than $3$ plus many composite numbers as well. The set forms a semigroup which is closed under multiplication.
The product I am generally interested in is the product of a consecutive series of members of $S$, $$\prod_{i=x}^y s_i$$ I note that this product can be represented as $$\frac{\prod_{i=1}^{y} s_i}{\prod_{i=1}^{x-1} s_i}$$ much like products of a particular set of consecutive integers can be represented as the quotient of two factorials. The specific product I am interested in is $$R_n=\prod_{s_a=p_n^2}^{s_b=p_{n+1}^2} s_i$$ where $p_n$ is the $n$th prime number, and in this context, $n>2$, that is, $p_n>3$.
The question I have about this product is: Can anything be said about the upper bound of the number of distinct prime factors of that product, that is $\max (\Omega(R_n))$ with respect to $p_n$?
Trivially, $\max (\Omega(R_n)) \le n$; but I suspect that in general it is significantly smaller than $n$. Other than hand calculating some small examples, I have made no headway on this.
I found this related question which appears to deal with a sum similar to $\sum_{i=1}^nR_i$, but not precisely relevant to any particular $R_n$, and the function $f(p)$ in that question runs over an interval bounded by primes and containing all integers, rather than an interval bounded by squares of primes and containing only members of $S$.
I am unaware of any general way to approach the question. Any thoughts or directions to pursue would be greatly appreciated.