5045589688 · 4933# + 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:5045589688 · 4933# + 1
Verification status (*):Proven
Official Comment (*):Cunningham chain 2nd kind (8p-7)
Proof-code(s): (*):p295 : Angel, NewPGen, OpenPFGW
Decimal Digits:2106   (log10 is 2105.8636686966)
Rank (*):104677 (digit rank is 2)
Entrance Rank (*):67279
Currently on list? (*):no
Submitted:12/15/2010 01:51:09 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:96940
Status Flags:none
Score (*):27.598 (normalized score 0)

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.
Cunningham Chains (2nd kind) (archivable class *)
Prime on list: no, rank 11, weight 42.859969944537
Subcategory: "Cunningham chain 2nd kind (8p-7)"
(archival tag id 213023, tag last modified 2023-03-11 15:53:59)

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_id96940
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 5045589688 4933 # 1 2>&1 [Elapsed time: 267.450 seconds]
modified2020-07-07 22:30:32
created2010-12-15 01:52:02
id123262

fieldvalue
prime_id96940
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"5045589688*4933#+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 5045589688*4933#+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 4943 Calling Brillhart-Lehmer-Selfridge with factored part 33.44% 5045589688*4933#+1 is prime! (2.1600s+0.0000s) [Elapsed time: 2.00 seconds]
modified2020-07-07 22:30:32
created2010-12-15 01:53:02
id123263

Query times: 0.0004 seconds to select prime, 0.0005 seconds to seek comments.
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