The nth Prime Page
will now find any of the first 2,623,557,157,654,233 primes or
) for x
up to 100,000,000,000,000,000.
- Currently on list?
- The value of this field (
prime.onlist) is either 'short', 'yes', or 'no'.
The list contains the 5000 largest known primes plus 20 (or 5) each of the archivable forms (or archivable classes respectively). If a
prime fails to meet these criteria it is labeled
'no'. The short list includes
those with more than 500,000 digits (as of Jan 2012), plus 20 (or 5) each of the archivable forms. So those
that do make the list are labeled
'short' if they make this short list, and
- Verification Status
- Only proven primes are allowed on this list! When possible we try to verify these proofs
independently. The verification status (
prime.prime) is one of the following:
- Proven composite-will soon be deleted from the database. This should never happen, but sometimes does.
- The verification process has not yet started. If a lot of primes were submitted at once the system may take
many hours to catch up.
- The system is working on this prime. If the prime is over a hundred thousand digits,
this might take a little while (sometimes days).
- We were able to verify it is a PRP by a Fermat type test, but have not
yet reconstructed a proof. This is common on ECPP proofs where the verification requires substantial effort even with a
certificate. It is our hope to eventually go back and verify each of these completely.
complete. the number has once again been proven prime.
- We use this only for those primes verified by others
(hence verified externally)-and this is done only in the case of the Mersennes (and similar primes) which are so large
they would tie up
the system for weeks (and are already carefully verified by others).
- A proof code list the persons, programs and projects involved in a proof.
- The largest prime has rank one, the next rank two... (When multiple primes have the same number of
digits, then the
digit rank shows how this prime ranks among those with the same number of
digit rank is just 1).
- Entrance rank
- As new primes are added, the rank of any given prime slowly drops. The 'entrance rank' is the rank the
prime had when it was first added--so it is its highest rank. This rank is less reliable on primes submitted
before 2000 because the submission time was less granular. In fact, for some primes submitted before 1
January 1997 we only know what year they were submitted.
- Removed (date)
- Primes eventually get pushed off the list by the new primes being added. For primes that have been pushed
off, and have no comments, 'removed' is the date/time at which they were pushed off. This feature has not yet
been implemented for primes with comments because that is much more difficult to do.
- A measure of how difficult it is to find primes of this size:
log((log n)3 log log n). See the bottom of the Top 20 by Score page for an explanation. The normalized
score is this score without the final (natural) log, divided by the same for the 5000th prime. See the bottom of
the page Top 20 by Normalized Score for more information
about normalized scores.