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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:12705   (log10 is 12704.5543927921)
Rank (*):70582 (digit rank is 4)
Entrance Rank (*):70043
Currently on list? (*):short
Submitted:11/12/2017 18:43:32 CDT
Last modified:11/12/2017 19:50:18 CDT
Database id:123988
Blob database id:379
Status Flags:Verify, TrialDiv
Score (*):33.1818 (normalized score 0)

Description: (from blob table id=379)

The number of unrestricted integer partitions of 130242827 is p(130242827).

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 69
Subcategory: "ECPP"
(archival tag id 218914, tag last modified 2018-03-14 05:50:22)
Partitions (archivable *)
Prime on list: yes, rank 5
Subcategory: "Partitions"
(archival tag id 218915, 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 (19 Nov 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 3584204593...9289187153 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N-1 BLS with factored part 0.08% and helper 0.04% (0.28% proof)

3584204593...9289187153 is Fermat and Lucas PRP! (10.0617s+0.0043s)
[Elapsed time: 10.00 seconds]
modified2017-11-12 19:21:11
created2017-11-12 19:21:01

machineUsing: Xeon 4c+4c 3.5GHz
notespfgw, llr
modified2017-11-12 18:51:01
created2017-11-12 18:51:01

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