primV(7577, - 1, 10692)
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At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: 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:

field (help)value
Description:primV(7577, - 1, 10692)
Verification status (*):PRP
Official Comment:Generalized Lucas primitive part
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):x33 : Carmody, Renze, Water, Broadhurst, Primo, OpenPFGW
Decimal Digits:25140   (log10 is 25139.142470395)
Rank (*):61596 (digit rank is 2)
Entrance Rank (*):22853
Currently on list? (*):short
Submitted:4/15/2007 15:39:14 CDT
Last modified:4/15/2007 16:28:41 CDT
Database id:80038
Status Flags:Verify
Score (*):35.2934 (normalized score 0.0002)

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 20
Subcategory: "Generalized Lucas primitive part"
(archival tag id 191786, tag last modified 2016-07-21 21:20:29)

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): 

CHG proof at 25140 digits and 26.08% factorization with details in http://physics.open.ac.uk/~dbroadhu/cert/b10692.zip and a certificate compressed to 25MB in http://physics.open.ac.uk/~dbroadhu/cert/b10692_cert.gp.gz

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_id80038
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/pfgw -o -f -q"primV(7577,-1,10692)" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
trial factoring to 7762304
primV(7577,-1,10692) has no small factor.
[Elapsed time: 16.619 seconds]
modified2007-04-21 22:36:37
created2007-04-15 15:52:01
id89184

fieldvalue
prime_id80038
person_id9
machineRedHat P4 P4
whatprp
notesCommand: /home/caldwell/client/pfgw -tc -q"primV(7577,-1,10692)" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing primV(7577,-1,10692) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 41
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(10240,21) to FFT(10240,20)
Reduced from FFT(10240,20) to FFT(10240,19)
Reduced from FFT(10240,19) to FFT(10240,18)
Reduced from FFT(10240,18) to FFT(10240,17)
167030 bit request FFT size=(10240,17)
Running N-1 test using base 61
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(10240,21) to FFT(10240,20)
Reduced from FFT(10240,20) to FFT(10240,19)
Reduced from FFT(10240,19) to FFT(10240,18)
Reduced from FFT(10240,18) to FFT(10240,17)
167030 bit request FFT size=(10240,17)
Running N+1 test using discriminant 71, base 23+sqrt(71)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(10240,21) to FFT(10240,20)
Reduced from FFT(10240,20) to FFT(10240,19)
Reduced from FFT(10240,19) to FFT(10240,18)
Reduced from FFT(10240,18) to FFT(10240,17)
167038 bit request FFT size=(10240,17)
Calling N-1 BLS with factored part 1.43% and helper 0.03% (4.31% proof)
primV(7577,-1,10692) is Fermat and Lucas PRP! (359.4600s+0.1500s)
[Elapsed time: 360 seconds]
modified2007-04-21 22:36:37
created2007-04-15 16:22:41
id89187

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.