U(5239, 1, 7350) - U(5239, 1, 7349)
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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:U(5239, 1, 7350) - U(5239, 1, 7349)
Verification status (*):PRP
Official Comment:Lehmer number
Unofficial Comments:This prime has 2 user comments below.
Proof-code(s): (*):CH10 : Batalov, Primo, OpenPFGW, CHG
Decimal Digits:27333   (log10 is 27332.756281023)
Rank (*):62757 (digit rank is 1)
Entrance Rank (*):60416
Currently on list? (*):short
Submitted:6/28/2017 15:26:24 CDT
Last modified:6/28/2017 15:50:28 CDT
Database id:123606
Status Flags:Verify, TrialDiv
Score (*):35.552 (normalized score 0.0002)

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.
Lehmer number (archivable *)
Prime on list: yes, rank 8
Subcategory: "Lehmer number"
(archival tag id 218767, tag last modified 2019-08-03 12:50:11)

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 (28 Jun 2017): 
A CHG proof using 26.69% N+1 factorization and 3.69% N-1 helper (including a Primo proof for primU(5239,1,7350) that makes for 22.86% of the N+1). FactorDB entry has the factorizations' data.

David Broadhurst writes (15 Jul 2017): 
Calling N+1 BLS with factored part 26.69% and helper 6.80% lucasU(5239,1,7350)-lucasU(5239,1,7349) is Fermat and Lucas PRP!

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
notesCommand: /home/caldwell/client/pfgw/pfgw64 -tc -q"lucasU(5239,1,7350)-lucasU(5239,1,7349)" 2>&1
PFGW Version [GWNUM 27.11]
Primality testing lucasU(5239,1,7350)-lucasU(5239,1,7349) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N-1 test using base 31
Running N+1 test using discriminant 47, base 4+sqrt(47)
Calling N-1 BLS with factored part 0.62% and helper 0.39% (2.24% proof)

lucasU(5239,1,7350)-lucasU(5239,1,7349) is Fermat and Lucas PRP! (72.0161s+0.0038s)
[Elapsed time: 72.00 seconds]
modified2017-08-07 13:02:22
created2017-06-28 15:31:01

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