356926524288 + 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:356926524288 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L3209 : McArdle, GenefX64, AthGFNSieve, PrimeGrid, LLR
Decimal Digits:2911151   (log10 is 2911150.111434)
Rank (*):136 (digit rank is 1)
Entrance Rank (*):11
Currently on list? (*):short
Submitted:7/25/2012 15:58:08 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:108492
Status Flags:none
Score (*):49.909 (normalized score 141.2657)

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 25
Subcategory: "Generalized Fermat"
(archival tag id 214445, tag last modified 2024-01-04 20:37:22)

User comments about this prime (disclaimer):

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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_id108492
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 1 356926 524288 1 2>&1 [Elapsed time: 8.911 seconds]
modified2020-07-07 22:30:25
created2012-07-25 16:05:02
id146569

fieldvalue
prime_id108492
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -t -q"356926^524288+1" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 356926^524288+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 54.01% 356926^524288+1 is prime! (1465510.5446s+0.2685s) [Elapsed time: 16.96 days]
modified2020-07-07 22:30:25
created2012-07-25 16:08:01
id146570

Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.
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