What is the largest known prime in sequence?

Question

As of writing, 2^82,589,933 &minus; 1 is the largest known prime, but do we know all of the primes lower than it? If not, what is the largest known prime in sequence, without gaps?

philomath_mn · Accepted Answer

This [1] is a good comment explaining why we will never know all the primes up to the largest known prime.
I am having a surprisingly hard time finding the answer to the second part of your question. This site [2] samples the first 50 million primes, and the OEIS tracks this sequence as A000040 [3] but they provide a very short list. No luck finding the longest computed A000040 sequence so far.
EDIT:
The research on the Golbach Conjecture summarized here [4] found all the primes up to 10^18, that is the most I am finding so far.
[1]: https://www.reddit.com/r/math/comments/21nclc/comment/cgepan...
[2]: https://primes.utm.edu/lists/small/millions/
[3]: https://oeis.org/A000040
[4]: http://sweet.ua.pt/tos/goldbach.html

OJFord · Answer

Is it possible to verify a prime without knowing all smaller primes by corollary at least?

vemodalen · Answer

For Mersenne primes M(57 885 161) is the largest without a gap [0]
There is tracking of these [1]
[0] https://www.mersenneforum.org/showthread.php?p=595056#post59...
[1] https://www.mersenne.org/report_milestones/

kadoban · Answer

We certainly do not know all primes lower than it. Our universe could not contain the answer of writing them all out.I'm not sure the answer of the second part.

What is the largest known prime in sequence?

As of writing, 2^82,589,933 − 1 is the largest known prime, but do we know all of the primes lower than it? If not, what is the largest known prime in sequence, without gaps?

Is it possible to verify a prime without knowing all smaller primes by corollary at least?

For Mersenne primes M(57 885 161) is the largest without a gap [0]
There is tracking of these [1]
[0] https://www.mersenneforum.org/showthread.php?p=595056#post59...
[1] https://www.mersenne.org/report_milestones/

We certainly do not know all primes lower than it. Our universe could not contain the answer of writing them all out.
I'm not sure the answer of the second part.

What is the largest known prime in sequence?

As of writing, 2^82,589,933 − 1 is the largest known prime, but do we know all of the primes lower than it? If not, what is the largest known prime in sequence, without gaps?

Is it possible to verify a prime without knowing all smaller primes by corollary at least?

For Mersenne primes M(57 885 161) is the largest without a gap [0]There is tracking of these [1][0] https://www.mersenneforum.org/showthread.php?p=595056#post59...[1] https://www.mersenne.org/report_milestones/

We certainly do not know all primes lower than it. Our universe could not contain the answer of writing them all out.I'm not sure the answer of the second part.

For Mersenne primes M(57 885 161) is the largest without a gap [0]
There is tracking of these [1]
[0] https://www.mersenneforum.org/showthread.php?p=595056#post59...
[1] https://www.mersenne.org/report_milestones/

We certainly do not know all primes lower than it. Our universe could not contain the answer of writing them all out.
I'm not sure the answer of the second part.