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: 5188804465536 + 1 Verification status (*): Proven Official Comment: Generalized Fermat Proof-code(s): (*): L4760 : Sipes, GFNSvCUDA, GeneFer, AthGFNSieve, PrimeGrid, LLR Decimal Digits: 505615   (log10 is 505614.65054671) Rank (*): 2740 (digit rank is 1) Entrance Rank (*): 2239 Currently on list? (*): yes Submitted: 2/10/2019 21:44:48 CDT Last modified: 2/10/2019 23:50:11 CDT Database id: 126071 Status Flags: TrialDiv Score (*): 44.5394 (normalized score 1.61)

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: no, rank 455
Subcategory: "Generalized Fermat"
(archival tag id 220078, tag last modified 2019-11-17 12:50:09)

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 126071 person_id 9 machine Using: Xeon 4c+4c 3.5GHz what prime notes Command: /home/caldwell/client/pfgw/pfgw64 -t -q"51888044^65536+1" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 51888044^65536+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 43.51% 51888044^65536+1 is prime! (5531.3523s+0.0146s) [Elapsed time: 1.54 hours] modified 2019-02-10 23:23:13 created 2019-02-10 21:51:02 id 171748