563528 · 13563528 - 1
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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:563528 · 13563528 - 1
Verification status (*):Proven
Official Comment:Generalized Woodall
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p262 : Vogel, Gcwsieve, MultiSieve, PrimeGrid, OpenPFGW
Decimal Digits:627745   (log10 is 627744.02035427)
Rank (*):1306 (digit rank is 1)
Entrance Rank (*):65
Currently on list? (*):short
Submitted:12/8/2009 10:18:57 CDT
Last modified:12/11/2009 05:50:21 CDT
Database id:91121
Status Flags:none
Score (*):45.2038 (normalized score 3.6366)

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 Woodall (archivable *)
Prime on list: yes, rank 5
Subcategory: "Generalized Woodall"
(archival tag id 210565, tag last modified 2015-05-01 14:20:30)

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.

PrimeGrid writes (11 Sep 2014): 
For more information, please see the Official Announcement.

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.
machineDitto P4 P4
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 563528 13 563528 -1 2>&1
[Elapsed time: 9.545 seconds]
modified2011-12-27 16:48:41
created2009-12-08 10:35:12

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -tp -q"563528*13^563528-1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 563528*13^563528-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(262144,19) to FFT(262144,18)
Reduced from FFT(262144,18) to FFT(262144,17)
Reduced from FFT(262144,17) to FFT(262144,16)
4170658 bit request FFT size=(262144,16)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
563528*13^563528-1 is prime! (-156.0986s+0.1500s)
[Elapsed time: 2.80 days]
modified2010-03-13 18:56:32
created2009-12-08 10:23:01

Query times: 0.0004 seconds to select prime, 0.0009 seconds to seek comments.