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: 52712138131072 + 1 Verification status (*): Proven Official Comment: Generalized Fermat Proof-code(s): (*): L4819 : Inci, GFNSvCUDA, GeneFer, AthGFNSieve, PrimeGrid, LLR Decimal Digits: 1012127   (log10 is 1012126.2702947) Rank (*): 475 (digit rank is 1) Entrance Rank (*): 312 Currently on list? (*): short Submitted: 8/11/2018 01:25:04 CDT Last modified: 8/11/2018 07:50:17 CDT Database id: 125534 Status Flags: TrialDiv Score (*): 46.67 (normalized score 13.4694)

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 114
Subcategory: "Generalized Fermat"
(archival tag id 219870, tag last modified 2019-12-01 21:20:26)

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 125534 person_id 9 machine Using: Xeon 4c+4c 3.5GHz what prime notes Command: /home/caldwell/client/pfgw/pfgw64 -t -q"52712138^131072+1" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 52712138^131072+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 55.31% 52712138^131072+1 is prime! (22485.4780s+0.0330s) [Elapsed time: 6.25 hours] modified 2018-09-25 13:41:11 created 2018-08-11 01:31:01 id 171208