primA(170575)
(Another of the Prime Pages' resources)
The Largest Known Primes Icon
  View this page in:   language help
 
GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

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:primA(170575)
Verification status (*):PRP
Official Comment:Lucas Aurifeuillian primitive part, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c77 : Batalov, Primo
Decimal Digits:14258   (log10 is 14257.047717309)
Rank (*):69908 (digit rank is 2)
Entrance Rank (*):69402
Currently on list? (*):short
Submitted:12/30/2018 21:04:32 CDT
Last modified:12/30/2018 21:20:25 CDT
Database id:125893
Status Flags:Verify, TrialDiv
Score (*):33.5388 (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 Aurifeuillian primitive part (archivable *)
Prime on list: yes, rank 5
Subcategory: "Lucas Aurifeuillian primitive part"
(archival tag id 220015, tag last modified 2019-04-07 01:20:28)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 70
Subcategory: "ECPP"
(archival tag id 220016, tag last modified 2019-04-07 01:20:26)

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 (30 Dec 2018): 
Certificate is available at FactorDB

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_id125893
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprp
notesPFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11]
Primality testing 1116136494...9067991551 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 23, base 2+sqrt(23)
Calling N-1 BLS with factored part 0.25% and helper 0.10% (0.86% proof)


1116136494...9067991551 is Fermat and Lucas PRP! (15.2516s+0.0748s)
[Elapsed time: 15.00 seconds]
modified2018-12-30 21:11:17
created2018-12-30 21:11:02
id171570

fieldvalue
prime_id125893
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatrequested
notespfgw, llr
modified2018-12-30 21:11:01
created2018-12-30 21:11:01
id171569

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