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: 28782838101 · 2333333 - 1 Verification status (*): Proven Official Comment: Arithmetic progression (3,d=3371818539*2^333335) [g282] Proof-code(s): (*): L453 : Straubinger1, NewPGen, PrimeGrid, TPS, LLR Decimal Digits: 100354   (log10 is 100353.69067828) Rank (*): 41113 (digit rank is 724) Entrance Rank (*): 4308 Currently on list? (*): no Submitted: 12/25/2007 14:47:13 CDT Last modified: 1/4/2008 08:40:48 CDT Database id: 83392 Status Flags: none Score (*): 39.5651 (normalized score 0.0122)

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.

Arithmetic Progressions of Primes (archivable class *)

Prime on list: no, rank 29, weight 46.2946143816889
Subcategory: "Arithmetic progression (3,d=*)"
(archival tag id 188193, tag last modified 2017-02-02 09:20:09)

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 83392 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 28782838101 2 333333 -1 2>&1 [Elapsed time: 9.294 seconds] modified 2011-12-27 16:48:48 created 2007-12-25 14:52:40 id 95896

field value prime_id 83392 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/llr.pl 28782838101*2^333333-1 2>&1 Starting Lucas Lehmer Riesel prime test of 28782838101*2^333333-1 V1 = 5 ; Computing U0... Done Computing U0. Starting Lucas-Lehmer loop... 28782838101*2^333333-1 is prime! Time: 1275.954 sec. [Elapsed time: 21.27 minutes] modified 2008-01-03 10:54:42 created 2007-12-25 16:08:44 id 95905