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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
Verification status (*):PRP
Official Comment:Partitions, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c85 : Lasher, Broadhurst, Primo
Decimal Digits:12699   (log10 is 12698.7086208804)
Rank (*):70808 (digit rank is 1)
Entrance Rank (*):69411
Currently on list? (*):short
Submitted:3/29/2017 08:48:05 CDT
Last modified:3/29/2017 09:50:26 CDT
Database id:123228
Blob database id:364
Status Flags:Verify, TrialDiv
Score (*):33.1803 (normalized score 0)

Description: (from blob table id=364)

The number of unrestricted integer partitions of 130123073 is p(130123073).

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.
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 81
Subcategory: "ECPP"
(archival tag id 218681, tag last modified 2018-06-16 15:20:23)
Partitions (archivable *)
Prime on list: yes, rank 10
Subcategory: "Partitions"
(archival tag id 218682, tag last modified 2017-11-12 19:50:21)

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 (2 Apr 2017): 

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.
machineUsing: Xeon 4c+4c 3.5GHz
notesPFGW Version [GWNUM 27.11]
Primality testing 5112353551...5200125401 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 19, base 2+sqrt(19)
Calling N+1 BLS with factored part 0.02% and helper 0.02% (0.09% proof)

5112353551...5200125401 is Fermat and Lucas PRP! (10.1875s+0.0040s)
[Elapsed time: 10.00 seconds]
modified2017-03-31 15:53:56
created2017-03-29 09:21:01

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.