At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important PrimePages database: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.

Verification status (*):PRP
Official Comment (*):Partitions, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c59 : Metcalfe, OpenPFGW, Primo
Decimal Digits:11677   (log10 is 11676.572137813)
Rank (*):76055 (digit rank is 2)
Entrance Rank (*):65486
Currently on list? (*):short
Submitted:2/25/2014 15:20:48 CDT
Last modified:2/27/2014 08:22:15 CDT
Database id:117287
Blob database id:307
Status Flags:Verify, TrialDiv
Score (*):32.9204 (normalized score 0)

title='from prime_blob table' id='blob'>Description: (from blob table id=307)

The number of partitions of 110030755 is p(110030755).

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 137
Subcategory: "ECPP"
(archival tag id 217630, tag last modified 2021-05-04 10:20:37)
Partitions (archivable *)
Prime on list: yes, rank 19
Subcategory: "Partitions"
(archival tag id 217631, tag last modified 2020-02-10 21:20:08)

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 Metcalfe writes (11 Sep 2014):  (report abuse)
Certificate available from here.

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.
machineWinXP Dual Core 2.6GHz 64-bit Laptop
notesCommand: pfgw64.exe -tc p_117287.txt 2>&1 PFGW Version [GWNUM 27.8] Primality testing 3733686184...3513537247 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N-1 test using base 5 Running N+1 test using discriminant 11, base 2+sqrt(11) Calling N+1 BLS with factored part 0.08% and helper 0.02% (0.27% proof) 3733686184...3513537247 is Fermat and Lucas PRP! (15.6269s+0.0369s) [Elapsed time: 16 seconds]
modified2020-07-07 17:30:17
created2014-02-27 08:10:58

Query times: 0.0004 seconds to select prime, 0.0012 seconds to seek comments.
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