Yes. Alas, mathematicians not in number theory tend to have p-ness envy.
A more troubling example of imposing this world view is decomposing 3-manifolds, where people like to think of S^1 x S^2 as prime. This only makes sense as a form of respect for one's elders.
One constructs 3-manifolds by gluing irreducible manifolds together after cutting out balls; one needs S^3 itself to express self-loops in this gluing graph, if there are no other pieces. S^1 x S^2 is S^3 with one self-loop. But the interest is in the pieces, not the graph (which can be freely reorganized), unless one aspires to be a number theorist.
