- 30 · Bern(3176)/(169908471493279 · 905130251538800883547330531 · 434990809309147283469396721753169)

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.

Description: - 30 · Bern(3176)/(169908471493279 · 905130251538800883547330531 · 434990809309147283469396721753169)
Verification status (*):PRP
Official Comment (*):Irregular, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c63 : Ritschel, TOPS, Primo
Decimal Digits:7138   (log10 is 7137.7366983683)
Rank (*):81417 (digit rank is 1)
Entrance Rank (*):75089
Currently on list? (*):short
Submitted:11/18/2016 01:52:57 CDT
Last modified:11/18/2016 02:20:37 CDT
Database id:122507
Status Flags:Verify, TrialDiv
Score (*):31.3944 (normalized score 0)

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.
Irregular Primes (archivable *)
Prime on list: yes, rank 11
Subcategory: "Irregular Primes"
(archival tag id 218513, tag last modified 2021-05-01 12:20:47)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 334
Subcategory: "ECPP"
(archival tag id 218514, tag last modified 2021-09-18 09:37:41)

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.

Thomas Ritschel writes (18 Nov 2016):  (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.
machineUsing: Xeon (pool) 4c+4c 3.5GHz
notesPFGW Version [GWNUM 27.11] Primality testing 5453789460...5240246021 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 17, base 3+sqrt(17) Calling N-1 BLS with factored part 0.13% and helper 0.05% (0.46% proof) 5453789460...5240246021 is Fermat and Lucas PRP! (3.2524s+0.0520s) [Elapsed time: 3.00 seconds]
modified2020-07-07 17:30:16
created2016-11-18 01:53:03

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