# FAQ: What is the longest list of primes?

### By Chris Caldwell

It is often wondered what is the longest
list of consecutive primes, starting at two, that has ever been found? Sometimes
it is asked in a different manner: "what is the smallest number *n*
such that it is not known whether or not *n* is prime?" (Of course
there are infinitely many primes,
so there is no theoretical limit to the length of such a list.)

Perhaps the longest lists ever calculated (but not all stored) are those corresponding to the mximal prime gape (and twin prime constant) projects. See
Nicely's lists. At the time I last updated this page, these projects had found (but not stored) all the prime up
to 10^{18}, but not yet to 10^{19}.

The problem with answering this question is **small primes are too easy
to find**. The can be found far faster than they can be read from a
hard disk, so no one bothers to keep long lists (say past 10^{9}).
Long lists just waste storage, and if placed on the Internet, they just waste bandwidth. Nevertheless,
due to popular demand, I have placed several lists on this
site, such as the first 100,008 primesand the first fifty million primes.

If you want an even longer list, run a sieve program on your machine. Folks quite regularly resieve to find all the primes up to 1,000,000,000,000, this should take well less than a minute.

**The answer to the second form of the question is similar.** If we could
give the smallest number *n* such that it is not known whether or
not *n* is prime, then someone could check the next million primes
in about a second of computer time (at most!).