Collatz Conjecture, can the following skip a prime number?

Following my previous questions at: Collatz Conjecture, why an increment of $+6$ in the following? and Collatz Conjecture, why a rate of change of $*4$ in the following?

Following the rules of the Collatz Conjecture, in this experiment I have created a list of all odd numbers until $$33333$$. The list includes 3 columns, such as in the following sample:

A) Starting Odd $$(X)$$ B) $$(X * 3) +1$$ C) $$X/2$$ repeat until odd
1 4 2, (1)
3 10 (5)
5 16 8, 4, 2, (1)
7 22 (11)
9 28 14, (7)
11 34 (17)
13 40 20, 10, (5)
15 46 (23).
17 52 26 (13)
19 58 (29)
21 64 32, 16, 8, 2. (1)
23 70 (35)
25 76 38, (19)

...

You will notice that all the final odd results in column C) represent a list of all the prime numbers. as denoted in the () in column C): 1, 5, 7, 11, 13, 17, 19, 23, 29.

Is it possible to skip a prime number in that list (with the exception of $$3$$)?

No, you should actually get every odd number which isn't a multiple of $$3$$ (and, in particular, every odd prime save $$3$$).
Note that any prime $$p\ne2,3$$ is either $$1$$ or $$5$$ mod $$6$$. Suppose $$p=6k+5$$. Then set $$X=4k+3$$, so that $$3X+1=12k+10$$ and dividing by $$2$$ gives $$6k+5=p$$. Now suppose $$p=6k+1$$. Then let $$X=8k+1$$, so that $$3X+1=24k+4$$. Dividing by $$2$$ twice gives $$6k+1=p$$, as desired.
In fact, since nothing here depends on $$p$$ being prime, this shows that any odd number which isn't a multiple of $$3$$ is a final number in your column (c).
Conversely, note that no multiple of $$3$$ can ever be a final number in (c). (In fact, no multiple of $$3$$ can ever be an element in that column!) After all, if $$X=2k+1$$, then the final number is of the form $$2^{-n}(6k+4)$$. Note that $$6k+4$$ isn't divisible by $$3$$, and so no number in the last column can be of the form $$3k$$.