(6475815373 - 1)/64757
(Another of the Prime Pages' resources)
The Largest Known Primes Icon
  View this page in:   language help
 

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:(6475815373 - 1)/64757
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:73960   (log10 is 73959.20257338)
Rank (*):45641 (digit rank is 1)
Entrance Rank (*):45123
Currently on list? (*):short
Submitted:1/24/2018 22:46:21 CDT
Last modified:1/24/2018 23:20:09 CDT
Database id:124182
Status Flags:Verify, TrialDiv
Score (*):38.6245 (normalized score 0.0053)

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 3
Subcategory: "Generalized Repunit"
(archival tag id 218981, tag last modified 2018-01-24 23:20:10)

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 (24 Jan 2018): 
For details of the N-1 primality proof, see:
http://xenon.stanford.edu/~tjw/pp/64758_15373/index.html
N-1 was factored to 32%, and the KP proof used 30.44%. This proof also relies on an ECPP certificate of a 20770-digit helper prime that divides 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_id124182
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprp
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tc -q"(64758^15373-1)/64757" 2>&1
PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11]
Primality testing (64758^15373-1)/64757 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N-1 BLS with factored part 0.22% and helper 0.01% (0.68% proof)


(64758^15373-1)/64757 is Fermat and Lucas PRP! (482.2038s+0.0654s)
[Elapsed time: 8.05 minutes]
modified2018-01-24 23:01:04
created2018-01-24 22:53:01
id169846

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