Pocklington's Theorem
Let n-1=FR where F is the factored part of a number
| F=p_1^(a_1)...p_r^(a_r), |
(1)
|
where (R,F)=1, and R<sqrt(n).
Pocklington's theorem, also known as the Pocklington-Lehmer test, then says that if there exists a b_i for i=1, ..., r such that
| b_i^(n-1)=1 (mod n) |
(2)
|
and
| GCD(b_i^((n-1)/p_i)-1,n)=1, |
(3)
|
then n is prime.
See also
Pocklington's CriterionExplore with Wolfram|Alpha
WolframAlpha
More things to try:
Cite this as:
Weisstein, Eric W. "Pocklington's Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PocklingtonsTheorem.html