primV(44368, 1, 9504)

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:primV(44368, 1, 9504)
Verification status (*):PRP
Official Comment (*):Generalized Lucas primitive part
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):CH3 : Broadhurst, Water, OpenPFGW, Primo, CHG
Decimal Digits:26768   (log10 is 26767.1223476)
Rank (*):70561 (digit rank is 3)
Entrance Rank (*):18210
Currently on list? (*):short
Submitted:9/19/2005 13:43:35 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:75632
Status Flags:Verify
Score (*):35.4874 (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.
Generalized Lucas primitive part (archivable *)
Prime on list: yes, rank 15
Subcategory: "Generalized Lucas primitive part"
(archival tag id 191465, tag last modified 2023-03-11 15:53:59)

User comments about this prime (disclaimer):

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Chris Caldwell writes (12 May 2021):  (report abuse)
CHG proof with ECPP helpers.

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_id75632
person_id9
machineLinux P4 2.8GHz
whatprp
notesCommand: /home/caldwell/client/pfgw -f -tc -q"primV(44368,1,9504)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing primV(44368,1,9504) [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 8304036 Running N-1 test using base 61 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(12288,21) to FFT(12288,20) Reduced from FFT(12288,20) to FFT(12288,19) Reduced from FFT(12288,19) to FFT(12288,18) Reduced from FFT(12288,18) to FFT(12288,17) Reduced from FFT(12288,17) to FFT(12288,16) 177846 bit request FFT size=(12288,16) Running N+1 test using discriminant 71, base 2+sqrt(71) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(12288,21) to FFT(12288,20) Reduced from FFT(12288,20) to FFT(12288,19) Reduced from FFT(12288,19) to FFT(12288,18) Reduced from FFT(12288,18) to FFT(12288,17) Reduced from FFT(12288,17) to FFT(12288,16) 177854 bit request FFT size=(12288,16) Calling N-1 BLS with factored part 1.52% and helper 0.01% (4.58% proof) primV(44368,1,9504) is Fermat and Lucas PRP! (906.7747s+0.3583s) [Elapsed time: 908 seconds]
modified2020-07-07 22:30:43
created2005-09-19 16:02:52
id80803

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