I was playing around with collatz sequence stuff recently, and I made a plot of seed values vs the maximum value the seed's collatz sequence will reach. Highlighting primes in a logarithmic graph gives an interesting result
In this image, we evaluate the collatz sequences of all numbers ("seed values") from $1$ to $10^5$, and find the maximum number within each sequence. We plot each seed value on the $x$ axis with its corresponding maximum number in its sequence on the $y$ axis.
Then, highlight all points corresponding to a prime seed value red, and a composite blue.
As seen in the graph, the prime numbers seem to have a consistently larger "lower bound" for their maximum values than composites.
What causes this behavior?
My initial thought was that for composites highly divisible by 2 and have numbers in its sequence that are highly divisible by 2, the maximum value is itself, hence making up the very bottom of the graph. Meanwhile, a prime is always odd so the smallest possible number in its sequence is itself scaled up by $\frac32$.
Is this the correct explanation, or is there something else I am missing?