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: 475856524288 + 1 Verification status (*): Proven Official Comment: Generalized Fermat Proof-code(s): (*): L3230 : Kumagai, GeneferCUDA, AthGFNSieve, PrimeGrid, LLR Decimal Digits: 2976633   (log10 is 2976632.30096902) Rank (*): 12 (digit rank is 1) Entrance Rank (*): 11 Currently on list? (*): short Submitted: 8/14/2012 20:50:21 CDT Last modified: 8/24/2012 00:40:15 CDT Database id: 108818 Status Flags: none Score (*): 49.9772 (normalized score 1286.0626)

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.

Generalized Fermat (archivable *)

Prime on list: yes, rank 1
Subcategory: "Generalized Fermat"
(archival tag id 214459, tag last modified 2012-08-14 21:20:05)

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 108818 person_id 9 machine RedHat Virtual STEM Server what prime notes Command: /home/caldwell/client/pfgw -t -q"475856^524288+1" 2>&1 PFGW Version 3.3.4.20100405.x86_Stable [GWNUM 25.14] Primality testing 475856^524288+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 78.79% 475856^524288+1 is prime! (791256.0528s+0.4319s) [Elapsed time: 9.16 days] modified 2012-09-15 19:04:20 created 2012-08-14 20:52:36 id 147220

field value prime_id 108818 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 1 475856 524288 1 2>&1 [Elapsed time: 8.901 seconds] modified 2012-08-14 21:01:04 created 2012-08-14 20:52:02 id 147219