U(2341, - 1, 8819)

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:U(2341, - 1, 8819)
Verification status (*):PRP
Official Comment (*):Generalized Lucas number
Proof-code(s): (*):x25 : Broadhurst, Water, OpenPFGW, Primo
Decimal Digits:29712   (log10 is 29711.382364695)
Rank (*):63425 (digit rank is 1)
Entrance Rank (*):24704
Currently on list? (*):short
Submitted:4/29/2008 09:08:36 CDT
Last modified:4/29/2008 09:36:26 CDT
Database id:84889
Status Flags:Verify
Score (*):35.8098 (normalized score 0.0001)

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 Number (archivable *)
Prime on list: yes, rank 7
Subcategory: "Generalized Lucas Number"
(archival tag id 191238, tag last modified 2020-05-28 13:20:28)

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_id84889
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/pfgw -o -f -q"lucasU(2341,-1,8819)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] lucas trial factoring to 9289582 lucasU(2341,-1,8819) has no small factor. [Elapsed time: 22.917 seconds]
modified2020-07-07 17:30:39
created2008-04-29 09:22:01
id98905

fieldvalue
prime_id84889
person_id9
machineRedHat P4 P4
whatprp
notesCommand: /home/caldwell/client/pfgw -tc -q"lucasU(2341,-1,8819)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing lucasU(2341,-1,8819) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 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) 197408 bit request FFT size=(12288,17) Running N-1 test using base 7 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) 197408 bit request FFT size=(12288,17) Running N+1 test using discriminant 31, base 1+sqrt(31) 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) 197416 bit request FFT size=(12288,17) Running N+1 test using discriminant 31, base 2+sqrt(31) 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) 197416 bit request FFT size=(12288,17) Calling N-1 BLS with factored part 0.58% and helper 0.35% (2.08% proof) lucasU(2341,-1,8819) is Fermat and Lucas PRP! (795.6200s+0.0100s) [Elapsed time: 13.42 minutes]
modified2020-07-07 17:30:39
created2008-04-29 09:23:01
id98906

Query times: 0.0003 seconds to select prime, 0.0008 seconds to seek comments.
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