-2
$\begingroup$

This question already has an answer here:

As of December 2017, the largest known prime number was the Mersenne prime $2^{77232917} – 1$.

For such a large Mersenne prime, what are the techniques available for one to verify that it is in fact a prime? Is it simply a matter of brute force checking, or are there other more elegant techniques available?

$\endgroup$

marked as duplicate by Sil, Did, Lord Shark the Unknown, user99914, Eric Wofsey Aug 12 '18 at 14:52

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

3
$\begingroup$

Lucas–Lehmer primality test:

Let $p$ be an odd prime.

Define a sequence $\{s_i\}_{i \ge 0}$ by:

  1. $s_0 = 4$
  2. $s_{n+1} = s_n^2 - 2$

Then $2^p - 1$ is prime iff $s_{p-2} \equiv 0 \pmod {2^p - 1}$.

(For your case, $p = 77232917$.)

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.