18298534131072 + 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.

Description:18298534131072 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Proof-code(s): (*):L4201 : Brown1, GFNSvCUDA, GeneFer, AthGFNSieve, PrimeGrid, LLR
Decimal Digits:951900   (log10 is 951899.42892159)
Rank (*):833 (digit rank is 1)
Entrance Rank (*):698
Currently on list? (*):short
Submitted:2/25/2020 04:03:29 CDT
Last modified:2/25/2020 09:50:25 CDT
Database id:130645
Status Flags:TrialDiv
Score (*):46.4817 (normalized score 9.4082)

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 256
Subcategory: "Generalized Fermat"
(archival tag id 223878, tag last modified 2020-10-16 15:20:26)

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.
fieldvalue
prime_id130645
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"18298534^131072+1" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 18298534^131072+1 [N-1, Brillhart-Lehmer-Selfridge] F: 18298534^131072+1 59392/10019614 (trial factor to 374361749) F: 18298534^131072+1 124928/10019614 (trial factor to 374361749) F: 18298534^131072+1 190464/10019614 (trial factor to 374361749) F: 18298534^131072+1 256000/10019614 (trial factor to 374361749) Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 95.85% 18298534^131072+1 is prime! (19855.1477s+0.0320s) [Elapsed time: 5.52 hours]
modified2020-07-07 17:30:10
created2020-02-25 04:11:01
id176329

Query times: 0.0018 seconds to select prime, 0.0006 seconds to seek comments.
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