primV(56356)

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:primV(56356)
Verification status (*):PRP
Official Comment (*):Lucas primitive part, ECPP
Proof-code(s): (*):c74 : Lasher, Dubner, Primo
Decimal Digits:11557   (log10 is 11556.189702742)
Rank (*):76344 (digit rank is 2)
Entrance Rank (*):67403
Currently on list? (*):short
Submitted:2/5/2015 19:30:54 CDT
Last modified:2/5/2015 19:50:28 CDT
Database id:119237
Status Flags:Verify, TrialDiv
Score (*):32.8883 (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.
Lucas primitive part (archivable *)
Prime on list: yes, rank 20
Subcategory: "Lucas primitive part"
(archival tag id 217900, tag last modified 2021-02-13 15:20:13)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 146
Subcategory: "ECPP"
(archival tag id 217901, tag last modified 2021-06-05 07:37:29)

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.
fieldvalue
prime_id119237
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprp
notesPFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 1547756875...7283829761 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 29 Running N-1 test using base 31 Running N+1 test using discriminant 53, base 13+sqrt(53) Calling N-1 BLS with factored part 1.02% and helper 0.04% (3.11% proof) 1547756875...7283829761 is Fermat and Lucas PRP! (11.6052s+0.0036s) [Elapsed time: 11.00 seconds]
modified2020-07-07 17:30:17
created2015-02-05 19:31:02
id164843

Query times: 0.0005 seconds to select prime, 0.0007 seconds to seek comments.
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