8486092265536 + 1

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly.  This list is the most important PrimePages database: 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:

Description:8486092265536 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Proof-code(s): (*):L5059 : Kopp, GFNSvCUDA, GeneFer, AthGFNSieve, PrimeGrid, LLR
Decimal Digits:519616   (log10 is 519615.7908415)
Rank (*):7100 (digit rank is 1)
Entrance Rank (*):2571
Currently on list? (*):no
Submitted:2/21/2020 09:34:43 UTC
Last modified:5/20/2023 20:59:19 UTC
Removed (*):8/24/2022 21:57:17 UTC
Database id:130596
Status Flags:none
Score (*):44.6233 (normalized score 0.8303)

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 2962
Subcategory: "Generalized Fermat"
(archival tag id 223849, tag last modified 2023-10-02 20:37:13)

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.
machineUsing: Xeon 4c+4c 3.5GHz
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"84860922^65536+1" 2>&1 PFGW Version [GWNUM 29.8] Primality testing 84860922^65536+1 [N-1, Brillhart-Lehmer-Selfridge] F: 84860922^65536+1 104448/5462093 (trial factor to 197039202) F: 84860922^65536+1 225280/5462093 (trial factor to 197039202) F: 84860922^65536+1 346112/5462093 (trial factor to 197039202) Running N-1 test using base 5 Calling Brillhart-Lehmer-Selfridge with factored part 90.19% 84860922^65536+1 is prime! (5668.2614s+0.0170s) [Elapsed time: 1.57 hours]
modified2020-07-07 22:30:10
created2020-02-21 09:41:02

Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.
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