(V(5763, 1, 3753) + 1)/(V(5763, 1, 27) + 1)

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:(V(5763, 1, 3753) + 1)/(V(5763, 1, 27) + 1)
Verification status (*):PRP
Official Comment (*):Lehmer primitive part
Proof-code(s): (*):x25 : Broadhurst, Water, OpenPFGW, Primo
Decimal Digits:14013   (log10 is 14012.176707838)
Rank (*):73121 (digit rank is 1)
Entrance Rank (*):48713
Currently on list? (*):short
Submitted:5/19/2011 11:25:51 CDT
Last modified:5/19/2011 11:50:29 CDT
Database id:100130
Status Flags:Verify
Score (*):33.4851 (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.
Lehmer primitive part (archivable *)
Prime on list: yes, rank 18
Subcategory: "Lehmer primitive part"
(archival tag id 213236, tag last modified 2019-08-26 13:20:28)

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_id100130
person_id9
machineRedHat Virtual STEM Server
whatprp
notesCommand: /home/caldwell/client/pfgw -tc -q"(lucasV(5763,1,3753)+1)/(lucasV(5763,1,27)+1)" 2>&1 PFGW Version 3.3.4.20100405.x86_Stable [GWNUM 25.14] Primality testing (lucasV(5763,1,3753)+1)/(lucasV(5763,1,27)+1) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 23 Running N-1 test using base 59 Running N+1 test using discriminant 71, base 5+sqrt(71) Calling N-1 BLS with factored part 2.23% and helper 0.07% (6.76% proof) (lucasV(5763,1,3753)+1)/(lucasV(5763,1,27)+1) is Fermat and Lucas PRP! (67.3309s+0.0108s) [Elapsed time: 67.00 seconds]
modified2020-07-07 17:30:31
created2011-05-19 11:27:33
id129830

fieldvalue
prime_id100130
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/pfgw -o -f -q"(lucasV(5763,1,3753)+1)/(lucasV(5763,1,27)+1)" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] (lucasV(5763,1,3....sV(5763,1,27)+1) 1/1 mro=0 trial factoring to 4136128 (lucasV(5763,1,3753)+1)/(lucasV(5763,1,27)+1) has no small factor. [Elapsed time: 5.168 seconds]
modified2020-07-07 17:30:31
created2011-05-19 11:35:01
id129831

Query times: 0.0002 seconds to select prime, 0.0005 seconds to seek comments.
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