Let be an odd prime, be an integer such that and , and

Then the following are equivalent

1. is prime.

2. There exists an such that ,

where GCD is the greatest common divisor (i.e., and are relatively prime). This is a modified version of the original theorem due to Lehmer.

More things to try:

Weisstein, Eric W. "Pocklington's Criterion." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PocklingtonsCriterion.html