Pocklington's Theorem

Let $n-1=FR$ where $F$ is the factored part of a number

$$F={p_1}^{a_1} \cdots {p_r}^{a_r},$$ (1)

where $(R,F)=1$, and $R<\sqrt{n}$. If there exists a $b_i$ for $i=1$, ..., $r$ such that

$${b_i}^{n-1}\equiv 1\ \left({{\rm mod\ } {n}}\right)$$ (2)

$${\rm GCD}({b_i}^{(n-1)/p_i}-1,n)=1,$$ (3)

then $n$ is a Prime.