482677032768 + 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:482677032768 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Proof-code(s): (*):p343 : Brown1, GeneFer, AthGFNSieve, PrimeGrid, OpenPFGW
Decimal Digits:219011   (log10 is 219010.05962553)
Rank (*):29109 (digit rank is 1)
Entrance Rank (*):4698
Currently on list? (*):no
Submitted:3/7/2012 01:13:40 UTC
Last modified:3/11/2023 15:54:10 UTC
Removed (*):3/19/2012 12:18:57 UTC
Database id:105400
Status Flags:none
Score (*):41.9676 (normalized score 0.0498)

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 4434
Subcategory: "Generalized Fermat"
(archival tag id 214230, tag last modified 2024-03-28 10:37:21)

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_id105400
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 1 4826770 32768 1 2>&1 [Elapsed time: 7.646 seconds]
modified2020-07-07 22:30:27
created2012-03-07 01:18:01
id140389

fieldvalue
prime_id105400
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"4826770^32768+1" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 4826770^32768+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 38.01% 4826770^32768+1 is prime! (6149.6761s+0.0132s) [Elapsed time: 1.71 hours]
modified2020-07-07 22:30:27
created2012-03-07 01:23:01
id140390

Query times: 0.0003 seconds to select prime, 0.0003 seconds to seek comments.
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