primV(205011)
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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(205011)
Verification status (*):PRP
Official Comment:Lucas primitive part
Unofficial Comments:This prime has 2 user comments below.
Proof-code(s): (*):x39 : Keller, Dubner, Broadhurst, Primo, OpenPFGW
Decimal Digits:28552   (log10 is 28551.891410952)
Rank (*):60457 (digit rank is 1)
Entrance Rank (*):29752
Currently on list? (*):short
Submitted:5/27/2009 20:19:25 CDT
Last modified:5/27/2009 20:50:35 CDT
Database id:88535
Status Flags:Verify
Score (*):35.6868 (normalized score 0.0003)

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.
Lucas primitive part (archivable *)
Prime on list: yes, rank 1
Subcategory: "Lucas primitive part"
(archival tag id 210451, tag last modified 2009-05-27 20:50:38)

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): 
certificate

David Broadhurst writes (11 Sep 2014): 
See posting in NMBRTHRY list

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_id88535
person_id9
machineDitto P4 P4
whattrial_divided
notesPFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
7787731182...2948505624.........7793071219040623 1/1


trial factoring to 8900600
7787731182...3792636801 has no small factor.
[Elapsed time: 91.038 seconds]
modified2011-12-27 16:48:43
created2009-05-27 20:35:03
id106437

fieldvalue
prime_id88535
person_id9
machineRedHat P4 P4
whatprp
notesPFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 7787731182...3792636801 [N-1/N+1, Brillhart-Lehmer-Selfridge]
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)
Reduced from FFT(12288,17) to FFT(12288,16)
189704 bit request FFT size=(12288,16)
Running N+1 test using discriminant 13, base 6+sqrt(13)
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)
Reduced from FFT(12288,17) to FFT(12288,16)
189712 bit request FFT size=(12288,16)
Calling N-1 BLS with factored part 1.15% and helper 0.00% (3.44% proof)
7787731182...3792636801 is Fermat and Lucas PRP! (403.3600s+0.0300s)
[Elapsed time: 6.73 minutes]
modified2009-05-27 20:29:47
created2009-05-27 20:23:03
id106435

Query times: 0.0004 seconds to select prime, 0.0003 seconds to seek comments.