- E(1078)/361898544439043

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: - E(1078)/361898544439043
Verification status (*):PRP
Official Comment (*):Euler irregular, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c4 : Broadhurst, Primo
Decimal Digits:2578   (log10 is 2577.0381014363)
Rank (*):97863 (digit rank is 5)
Entrance Rank (*):28287
Currently on list? (*):short
Submitted:2/13/2002 18:43:12 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:30622
Blob database id:29
Status Flags:Verify
Score (*):28.2272 (normalized score 0)

Description: (from blob table id=29)

Certificate for this number was FULLY validated! Total time used to validate certificate: 15h 26mn 26.665s There were 407 steps in the primality proof

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 804
Subcategory: "ECPP"
(archival tag id 175624, tag last modified 2024-07-11 00:37:12)
Euler Irregular primes (archivable *)
Prime on list: yes, rank 20
Subcategory: "Euler Irregular primes"
(archival tag id 175623, tag last modified 2023-10-06 17:37:13)

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.

David Broadhurst writes (11 Sep 2014):  (report abuse)

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.
machineLinux PII 200
notesPFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 5 Primality testing 1091695289...4337714287 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 17, base 1+sqrt(17) Calling N+1 BLS with factored part 0.15% and helper 0.01% (0.47% proof) 1091695289...4337714287 is Fermat and Lucas PRP! (67.940000 seconds)
modified2003-03-25 17:21:44
created2003-02-01 15:57:51

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