Ask HN: 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?
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...
If you do trial division in increasing order, you’ll find one (the smallest prime factor if n, which is n itself if n is prime), but if n is composite, you can avoid that by doing it in random order, or by starting near √n and working down (or up). That way, even if n has only two/three prime factors, you’ll find them/one of them, but that won’t tell you that they are/one of them is prime.
There is tracking of these [1]
[0] https://www.mersenneforum.org/showthread.php?p=595056#post59...
I'm not sure the answer of the second part.