primU(43653)

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:primU(43653)
Verification status (*):PRP
Official Comment (*):Fibonacci primitive part
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):CH7 : Broadhurst, OpenPFGW, CHG
Decimal Digits:6082   (log10 is 6081.6572765592)
Rank (*):83700 (digit rank is 1)
Entrance Rank (*):51221
Currently on list? (*):short
Submitted:5/25/2010 14:21:14 CDT
Last modified:5/25/2010 14:50:30 CDT
Database id:92848
Status Flags:Verify
Score (*):30.8974 (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.
Fibonacci Primitive Part (archivable *)
Prime on list: yes, rank 18
Subcategory: "Fibonacci Primitive Part"
(archival tag id 210695, tag last modified 2019-03-30 15:20:27)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

David Broadhurst writes (11 May 2021):  (report abuse)
Proven with 27.65% factorization and a CHG certificate.

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_id92848
person_id9
machineRedHat P4 P4
whatprp
notesPFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 4542307792...4727626501 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(2560,21) to FFT(2560,20) Reduced from FFT(2560,20) to FFT(2560,19) Reduced from FFT(2560,19) to FFT(2560,18) Reduced from FFT(2560,18) to FFT(2560,17) Reduced from FFT(2560,17) to FFT(2560,16) 40414 bit request FFT size=(2560,16) Running N-1 test using base 19 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(2560,21) to FFT(2560,20) Reduced from FFT(2560,20) to FFT(2560,19) Reduced from FFT(2560,19) to FFT(2560,18) Reduced from FFT(2560,18) to FFT(2560,17) Reduced from FFT(2560,17) to FFT(2560,16) 40414 bit request FFT size=(2560,16) Running N+1 test using discriminant 29, base 10+sqrt(29) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(2560,21) to FFT(2560,20) Reduced from FFT(2560,20) to FFT(2560,19) Reduced from FFT(2560,19) to FFT(2560,18) Reduced from FFT(2560,18) to FFT(2560,17) Reduced from FFT(2560,17) to FFT(2560,16) 40422 bit request FFT size=(2560,16) Calling N-1 BLS with factored part 1.79% and helper 0.00% (5.38% proof) 4542307792...4727626501 is Fermat and Lucas PRP! (22.1900s+0.0000s) [Elapsed time: 23.00 seconds]
modified2020-07-07 17:30:34
created2010-05-25 14:23:01
id115077

fieldvalue
prime_id92848
person_id9
machineDitto P4 P4
whattrial_divided
notesPFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] 4542307792...7522069599.........0310094773181374 1/1 trial factoring to 1677104 4542307792...4727626501 has no small factor. [Elapsed time: 4.174 seconds]
modified2020-07-07 17:30:34
created2010-05-25 14:35:01
id115079

Query times: 0.0005 seconds to select prime, 0.0011 seconds to seek comments.
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