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.

This prime's information:

Verification status (*):PRP
Official Comment (*):Partitions, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c77 : Batalov, Primo
Decimal Digits:12302   (log10 is 12301.277150387)
Rank (*):77152 (digit rank is 3)
Entrance Rank (*):66845
Currently on list? (*):no
Submitted:5/7/2015 00:06:12 CDT
Last modified:5/7/2015 11:20:29 CDT
Database id:119885
Blob database id:338
Status Flags:Verify
Score (*):33.0818 (normalized score 0)

Description: (from blob table id=338)

The number of unrestricted integer partitions of 122110618 is p(122110618).

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 206
Subcategory: "ECPP"
(archival tag id 218028, tag last modified 2022-11-14 11:36:29)
Partitions (archivable *)
Prime on list: no, rank 44
Subcategory: "Partitions"
(archival tag id 218029, tag last modified 2022-08-02 14:37:22)

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.

Serge Batalov writes (7 May 2015):  (report abuse)
Primo certificate is available at FactorDB.
numbpart(n) in Pari/GP is working well for sizes n ~ 10^8. For larger arguments, Arb implementation can be used.

For example, the smallest (PR)prime partition number p(n) with n>=10^10 is p(10^10+76282) = 27994222743945352244...15765421425294386781 (111391 digits).

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 1892999010...5859910237 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 5, base 5+sqrt(5) Calling N-1 BLS with factored part 0.13% and helper 0.01% (0.40% proof) 1892999010...5859910237 is Fermat and Lucas PRP! (9.8203s+0.0038s) [Elapsed time: 10.00 seconds]
modified2020-07-07 17:30:17
created2015-05-07 06:26:34

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