Explanation of Terms on the Page Displaying a Single Prime

Currently on list?

The value of this field (prime.onlist) is either '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 meets one of these criteria it is labeled 'yes'.  Otherwise, it is labeled 'no'.

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:

'Composite'

Proven composite-will soon be deleted from the database.  This should never happen, but sometimes does.

'Untested'

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.

'InProcess'

The system is working on this prime.  If the prime is over a hundred thousand digits, this might take a little while (sometimes days).

'PRP'

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.

'Proven'

Verification complete.  the number has once again been proven prime.

'External'

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).

Official comment

Certain forms of primes (see the top 20 index are allowed on the list at smaller sizes, ... and those that are such exceptions are marked with official comments within the prime list. These are distinct from the user comments.

Proof-code

A proof code list the persons, programs and projects involved in a proof.

Rank

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 digits--otherwise 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.

Score

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.