(185213477 - 1)/1851
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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
Description:(185213477 - 1)/1851
Verification status (*):PRP
Official Comment:Generalized repunit
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p170 : Wu_T, Primo, OpenPFGW
Decimal Digits:44035   (log10 is 44034.730112657)
Rank (*):52978 (digit rank is 1)
Entrance Rank (*):50185
Currently on list? (*):short
Submitted:8/1/2015 09:44:59 CDT
Last modified:8/1/2015 10:20:26 CDT
Database id:120181
Status Flags:Verify, TrialDiv
Score (*):37.0249 (normalized score 0.0012)

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.
Generalized Repunit (archivable *)
Prime on list: yes, rank 11
Subcategory: "Generalized Repunit"
(archival tag id 218070, tag last modified 2017-02-04 08:50:35)

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.

Tom Wu writes (1 Aug 2015): 
BLS primality proof (N-1)

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_id120181
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprp
notesCommand: /home/caldwell/client/pfgw/pfgw64 -tc -q"(1852^13477-1)/1851" 2>&1
PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11]
Primality testing (1852^13477-1)/1851 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N-1 test using base 19
Running N+1 test using discriminant 29, base 10+sqrt(29)
Calling N-1 BLS with factored part 0.11% and helper 0.00% (0.34% proof)


(1852^13477-1)/1851 is Fermat and Lucas PRP! (199.1772s+0.0008s)
[Elapsed time: 3.32 minutes]
modified2016-04-08 12:40:28
created2015-08-01 09:51:01
id165809

Query times: 0.0004 seconds to select prime, 0.0005 seconds to seek comments.