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: 9999993 · 10234006 - 1 Verification status (*): Proven Official Comment: Near-repdigit Proof-code(s): (*): L1958 : DUrso, Srsieve, OpenPFGW, NewPGen, LLR Decimal Digits: 234013   (log10 is 234012.9999997) Rank (*): 9345 (digit rank is 1) Entrance Rank (*): 1989 Currently on list? (*): no Submitted: 6/5/2011 01:39:28 CDT Last modified: 6/5/2011 05:20:22 CDT Database id: 100342 Status Flags: none Score (*): 42.1714 (normalized score 0.5272)

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.

Near-repdigit (archivable *)

Prime on list: no, rank 24
Subcategory: "Near-repdigit"
(archival tag id 213271, tag last modified 2013-04-16 22:50:31)

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 100342 person_id 9 machine RedHat Virtual STEM Server what prime notes Command: /home/caldwell/client/pfgw -tp -q"9999993*10^234006-1" 2>&1 PFGW Version 3.3.4.20100405.x86_Stable [GWNUM 25.14] Primality testing 9999993*10^234006-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 7, base 1+sqrt(7) Calling Brillhart-Lehmer-Selfridge with factored part 69.89% 9999993*10^234006-1 is prime! (12068.4673s+0.0681s) [Elapsed time: 3.35 hours] modified 2011-12-27 16:48:32 created 2011-06-05 01:43:39 id 130254

field value prime_id 100342 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 9999993 10 234006 -1 2>&1 [Elapsed time: 9.056 seconds] modified 2011-12-27 16:48:32 created 2011-06-05 01:48:02 id 130255