Pocklington primality test

In mathematics, the Pocklington–Lehmer primality test is a primality test devised by Henry Cabourn Pocklington and Derrick Henry Lehmer to decide whether a given number ${\displaystyle N}$ is prime. The output of the test is a proof that the number is prime or that primality could not be established.

The test relies on the Pocklington Theorem (Pocklington criterion) which is formulated as follows:

Let ${\displaystyle N>1}$ be an integer, and suppose there exist numbers a and q such that

q is prime, ${\displaystyle q\vert N-1}$ and ${\displaystyle q>{\sqrt {N}}-1}$

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