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: 10290253 - 2 · 10145126 - 1 Verification status (*): Proven Official Comment: Near-repdigit, Palindrome Proof-code(s): (*): p235 : Bedwell, OpenPFGW Decimal Digits: 290253   (log10 is 290253) Rank (*): 5082 (digit rank is 1) Entrance Rank (*): 1873 Currently on list? (*): short Submitted: 4/11/2012 05:07:30 CDT Last modified: 4/11/2012 17:50:24 CDT Database id: 106219 Status Flags: none Score (*): 42.8338 (normalized score 0.9877)

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: yes, rank 16
Subcategory: "Near-repdigit"
(archival tag id 214299, tag last modified 2013-04-16 22:50:31)

Palindrome (archivable *)

Prime on list: yes, rank 2
Subcategory: "Palindrome"
(archival tag id 214300, 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 106219 person_id 9 machine Ditto P4 P4 what prime notes Command: /home/ditto/client/pfgw -tp -q"10^290253-2*10^145126-1" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 10^290253-2*10^145126-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 3, base 1+sqrt(3) Calling Brillhart-Lehmer-Selfridge with factored part 34.95% 10^290253-2*10^145126-1 is prime! (44136.7571s+0.0184s) [Elapsed time: 12.26 hours] modified 2012-07-16 11:33:01 created 2012-04-11 05:08:02 id 142028

field value prime_id 106219 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/pfgw -o -f -q"10^290253-2*10^145126-1" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] 10^290253-2*10^145126-1 1/1 mro=0 trial factoring to 106133972 10^290253-2*10^145126-1 has no small factor. [Elapsed time: 2587.869 seconds] modified 2012-07-16 11:33:01 created 2012-04-11 05:18:01 id 142029