676754262144 + 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:676754262144 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L2975 : Loureiro, GeneferCUDA, AthGFNSieve, PrimeGrid, LLR
Decimal Digits:1528413   (log10 is 1528412.4598604)
Rank (*):273 (digit rank is 1)
Entrance Rank (*):23
Currently on list? (*):short
Submitted:2/13/2012 08:48:51 CDT
Last modified:2/17/2012 19:50:23 CDT
Database id:104592
Status Flags:none
Score (*):47.9342 (normalized score 32.3078)

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 64
Subcategory: "Generalized Fermat"
(archival tag id 214046, tag last modified 2021-10-09 23:37:19)

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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 1 676754 262144 1 2>&1 [Elapsed time: 8.563 seconds]
modified2020-07-07 17:30:28
created2012-02-13 08:52:02

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -t -q"676754^262144+1" 2>&1 PFGW Version [GWNUM 26.5] Primality testing 676754^262144+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 75.73% 676754^262144+1 is prime! (383467.2930s+0.1193s) [Elapsed time: 4.44 days]
modified2020-07-07 17:30:28
created2012-02-13 08:53:01

Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.