Phi(6437, 10)

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:Phi(6437, 10)
Verification status (*):PRP
Official Comment (*):Unique, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c47 : Chandler, Primo
Decimal Digits:6240   (log10 is 6239.9542425094)
Rank (*):83184 (digit rank is 1)
Entrance Rank (*):44205
Currently on list? (*):short
Submitted:11/1/2008 08:21:36 CDT
Last modified:11/3/2008 20:20:02 CDT
Database id:85700
Status Flags:Verify
Score (*):30.9772 (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.
Unique (archivable *)
Prime on list: yes, rank 20
Subcategory: "Unique"
(archival tag id 210376, tag last modified 2021-06-05 00:37:32)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 366
Subcategory: "ECPP"
(archival tag id 210375, tag last modified 2021-06-05 14:37:22)

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 Sep 2014):  (report abuse)
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_id85700
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/pfgw -o -f -q"Phi(6437,10)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 1724500 Phi(6437,10) has no small factor. [Elapsed time: 1.021 seconds]
modified2020-07-07 17:30:39
created2008-11-01 08:22:01
id100871

fieldvalue
prime_id85700
person_id9
machineRedHat P4 P4
whatprp
notesCommand: /home/caldwell/client/pfgw -t -q"Phi(6437,10)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing Phi(6437,10) [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(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) 41466 bit request FFT size=(2560,17) Running N-1 test using base 7 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) 41466 bit request FFT size=(2560,17) Running N-1 test using base 11 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) 41466 bit request FFT size=(2560,17) Running N-1 test using base 17 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) 41466 bit request FFT size=(2560,17) Calling Brillhart-Lehmer-Selfridge with factored part 1.27% Phi(6437,10) is PRP! (17.3800s+0.0000s) [Elapsed time: 17.00 seconds]
modified2020-07-07 17:30:39
created2008-11-01 08:23:02
id100872

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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