Analogies between number fields and function fields have inspired newdevelopments in number theory for a long time. We will discuss asurprising non-analogy related to the distribution of primes. Forinstance, it is expected that any irreducible in ${mathbf Z}[t]$ havingat least two relatively prime values will take prime values infinitelyoften. (An example is $t^2+1$, while a nonexample is $t^2+t+2$, since$n^2+n+2$ is always even.) The analogue in ${mathbf F}_p[x][t]$ isfalse, e.g., $t^8+x^3$ is irreducible in ${mathbf F}_2[x][t]$ but$g(x)^8+x^3$ is reducible in ${mathbf F}_2[x]$ for every $g(x)$.