"τ(5711090)"

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:"τ(5711090)"
Verification status (*):PRP
Official Comment (*):ECPP
Unofficial Comments:This prime has 2 user comments below.
Proof-code(s): (*):c65 : Lygeros, Rozier, Primo
Decimal Digits:16526   (log10 is 16525.819616423)
Rank (*):75936 (digit rank is 1)
Entrance Rank (*):59690
Currently on list? (*):no
Submitted:1/13/2014 15:04:19 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:116900
Blob database id:303
Status Flags:Verify
Score (*):33.9959 (normalized score 0)

Description: (from blob table id=303)

[This prime has a pre-calculated decimal expansion (linked blob)]

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 137
Subcategory: "ECPP"
(archival tag id 217579, tag last modified 2024-03-24 06:37:14)

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.

Chris Caldwell writes (11 Sep 2014):  (report abuse)
The site http://www.ellipsa.eu/ notes: "Certified by Dimitris Katsios, Nik Lygeros and Olivier Rozier (EU, 2013) Certificate: ecpp16526.7z (11.9 MB)."

David Broadhurst writes (11 Sep 2014):  (report abuse)
U(1432228477996772,571^11,1091)

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_id116900
person_id9
machineDitto P4 P4
whatprp
notesPFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 6601101687...3797165741 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 7, base 2+sqrt(7) Calling N-1 BLS with factored part 0.08% and helper 0.07% (0.32% proof) 6601101687...3797165741 is Fermat and Lucas PRP! (113.4282s+0.0065s) [Elapsed time: 1.90 minutes]
modified2020-07-07 22:30:18
created2014-01-13 15:08:01
id162411

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