At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.

This prime's information:

field (help) value Description: 150209! + 1 Verification status (*): Proven Official Comment: Factorial Proof-code(s): (*): p3 : Dohmen, OpenPFGW Decimal Digits: 712355   (log10 is 712354.37028954) Rank (*): 286 (digit rank is 1) Entrance Rank (*): 73 Currently on list? (*): short Submitted: 10/31/2011 08:21:31 CDT Last modified: 11/3/2011 03:21:05 CDT Database id: 102627 Status Flags: none Score (*): 45.592 (normalized score 7.6723)

Archival tags:

There are certain forms classed as archivable: these prime may (at times) remain on this list even if they do not make the Top 5000 proper.  Such primes are tracked with archival tags.

Factorial primes (archivable *)

Prime on list: yes, rank 1
Subcategory: "Factorial"
(archival tag id 213604, tag last modified 2011-11-03 03:21:07)

Verification data:

The Top 5000 Primes is a list for proven primes only. In order to maintain the integrity of this list, we seek to verify the primality of all submissions.  We are currently unable to check all proofs (ECPP, KP, ...), but we will at least trial divide and PRP check every entry before it is included in the list.

field value prime_id 102627 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -t -q"150209!+1" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 150209!+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 150211 Running N-1 test using base 150217 Calling Brillhart-Lehmer-Selfridge with factored part 33.45% 150209!+1 is prime! (240480.6224s+2.6547s) [Elapsed time: 2.78 days] modified 2011-12-27 16:48:27 created 2011-10-31 08:23:01 id 134845

field value prime_id 102627 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/TrialDiv/TrialDiv -q 1 150209 ! 1 2>&1 [Elapsed time: 59234.044 seconds] modified 2011-12-27 16:48:27 created 2011-10-31 08:35:02 id 134846