primU(67703)

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.

This prime's information:

Description:primU(67703)
Verification status (*):PRP
Official Comment (*):Fibonacci primitive part, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c77 : Batalov, Primo
Decimal Digits:13954   (log10 is 13953.827261573)
Rank (*):78872 (digit rank is 1)
Entrance Rank (*):69245
Currently on list? (*):short
Submitted:7/22/2018 05:13:38 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:125494
Status Flags:Verify
Score (*):33.4722 (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.
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 198
Subcategory: "ECPP"
(archival tag id 219855, tag last modified 2024-10-07 11:37:16)
Fibonacci Primitive Part (archivable *)
Prime on list: yes, rank 12
Subcategory: "Fibonacci Primitive Part"
(archival tag id 219856, tag last modified 2024-10-07 11:37:16)

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 (22 Jul 2018):  (report abuse)
Certificate at FactorDB (primality section)

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_id125494
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprp
notesPFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 6718333715...0509184601 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 17 Running N-1 test using base 29 Running N-1 test using base 83 Running N+1 test using discriminant 107, base 7+sqrt(107) Calling N-1 BLS with factored part 0.65% and helper 0.02% (1.98% proof) 6718333715...0509184601 is Fermat and Lucas PRP! (21.1793s+0.0015s) [Elapsed time: 21.00 seconds]
modified2020-07-07 22:30:14
created2018-07-22 05:21:02
id171168

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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