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: 10134809 - 1067404 - 1 Verification status (*): Proven Official Comment: Near-repdigit, palindrome Proof-code(s): (*): p235 : Bedwell, OpenPFGW Decimal Digits: 134809   (log10 is 134809) Rank (*): 25363 (digit rank is 1) Entrance Rank (*): 11444 Currently on list? (*): short Submitted: 11/24/2010 18:56:33 CDT Last modified: 11/24/2010 20:50:22 CDT Database id: 96565 Status Flags: none Score (*): 40.4742 (normalized score 0.0966)

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 58
Subcategory: "Near-repdigit"
(archival tag id 212993, tag last modified 2013-04-16 22:50:31)

Palindrome (archivable *)

Prime on list: yes, rank 17
Subcategory: "Palindrome"
(archival tag id 212994, tag last modified 2013-01-08 06:50:30)

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 96565 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/pfgw -o -f -q"10^134809-10^67404-1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 46890193 10^134809-10^67404-1 has no small factor. [Elapsed time: 471.686 seconds] modified 2011-12-27 16:48:36 created 2010-11-24 19:05:01 id 122516

field value prime_id 96565 person_id 9 machine RedHat Virtual STEM Server what prime notes Command: /home/caldwell/client/pfgw -tp -q"10^134809-10^67404-1" 2>&1 PFGW Version 3.3.4.20100405.x86_Stable [GWNUM 25.14] Primality testing 10^134809-10^67404-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 7, base 1+sqrt(7) Calling Brillhart-Lehmer-Selfridge with factored part 34.95% 10^134809-10^67404-1 is prime! (4302.1174s+0.0339s) [Elapsed time: 71.73 minutes] modified 2010-11-28 11:14:54 created 2010-11-24 19:17:24 id 122517