\[ \begin{array}{l} \text{1. If } n \text{ is a perfect power, i.e. if } n = a^{b} \text{ for some integers } a, b > 1, \text{ then } n \text{ is composite.} \\ \text{2. Let } r \text{ be the smallest integer satisfying } \text{ord}_r(n) > (\log_2 n)^2. \text{ If } r, n \text{ are not relatively prime, then } n \text{ is composite.} \\ \text{3. For all } 2 \leq a \leq \min(r, n-1), \text{ if } a \mid n, \text{ then } n \text{ is composite.} \\ \text{4. If } n \leq r, \text{ then } n \text{ is prime.} \\ \text{5. For all } a \in \{ 1, 2, \dots, \left\lfloor \sqrt{\phi(r)} \log_2 n \right\rfloor\}, \text{ if for some integer } x, \\ \text{ } (x + a)^n \neq x^n + a \pmod{x^r - 1, n}, \text{ then } n \text{ is composite.} \\ \text{6. If none of the previous steps were conclusive, then } n \text{ is prime.} \end{array} \]