E(676)/878618128969410121818976030235415670049335313139\
11504892717789158174298202475475590955674162377015

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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:E(676)/878618128969410121818976030235415670049335313139\
11504892717789158174298202475475590955674162377015
Verification status (*):PRP
Official Comment:Euler irregular, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c8 : Water, Broadhurst, Primo
Decimal Digits:1391   (log10 is 1390.8590865956)
Rank (*):96923 (digit rank is 2)
Entrance Rank (*):86383
Currently on list? (*):short
Submitted:2/16/2013 06:49:59 CDT
Last modified:2/16/2013 07:50:27 CDT
Database id:111255
Blob database id:293
Status Flags:Verify
Score (*):26.3034 (normalized score 0)

Description: (from blob table id=293)

[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.
Euler Irregular primes (archivable *)
Prime on list: yes, rank 19
Subcategory: "Euler Irregular primes"
(archival tag id 215081, tag last modified 2017-02-06 05:20:41)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 824
Subcategory: "ECPP"
(archival tag id 215082, tag last modified 2017-10-14 12:20:21)

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): 
certificate

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_id111255
person_id9
machineRedHat P4 P4
whattrial_divided
notesPFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
7229139337343211....2702518970625923 1/1 mro=0


trial factoring to 335831
7229139337...8970625923 has no small factor.
[Elapsed time: 0.325 seconds]
modified2013-02-16 12:06:20
created2013-02-16 06:52:02
id152780

fieldvalue
prime_id111255
person_id9
machineDitto P4 P4
whatprp
notesPFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing 7229139337...8970625923 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 5, base 1+sqrt(5)
Calling N+1 BLS with factored part 0.37% and helper 0.02% (1.17% proof)
7229139337...8970625923 is Fermat and Lucas PRP! (0.6130s+0.0005s)
[Elapsed time: 1.00 seconds]
modified2013-02-16 07:23:14
created2013-02-16 07:23:13
id152783

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.