Reductions to and from PRIME
Assuming you're talking about polynomial-time reductions, since PRIME is in $P$, you can reduce it to any non-trivial decision problem (for which there is at least one instance with answer YES and at least one instance with answer NO). Moreover, any problem in $P$ can be reduced to PRIME.

To reduce an instance $I$ of PRIME to an instance $I_Q$ of non trivial decision problem $Q$, let $Y_Q$ and $N_Q$ be a YES and a NO instance for $Q$, respectively. The reduction is as follows: solve $I$ using a polynomial-time algorithm for PRIME. Then, let

$$I_Q = \begin{cases}Y_Q &amp; \mbox{if $I$ is a YES instance}, \\ N_Q &amp; \mbox{if $I$ is a NO instance}.\end{cases}$$

To reduce an instance $I_Q$ of a problem $Q \in P$ to an instance $I$ of PRIME, solve $I_Q$ using a polynomial-time algorithm for $Q$ and define

$$I = \begin{cases}2 &amp; \mbox{if $I_Q$ is a YES instance}, \\ 1 &amp; \mbox{if $I_Q$ is a NO instance.}\end{cases}$$