- E(1174)/50550511342697072710795058639332351763
(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: - E(1174)/50550511342697072710795058639332351763
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:2829   (log10 is 2828.0190277619)
Rank (*):86352 (digit rank is 1)
Entrance Rank (*):75765
Currently on list? (*):short
Submitted:2/16/2013 06:38:40 CDT
Last modified:2/16/2013 07:50:27 CDT
Database id:111254
Blob database id:292
Status Flags:Verify
Score (*):28.5167 (normalized score 0)

Description: (from blob table id=292)

[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 11
Subcategory: "Euler Irregular primes"
(archival tag id 215079, tag last modified 2014-06-21 13:51:45)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 579
Subcategory: "ECPP"
(archival tag id 215080, tag last modified 2017-11-27 10:20:19)

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_id111254
person_id9
machineRedHat P4 P4
whattrial_divided
notesPFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
1044787004148092....5756035985897087 1/1 mro=0


trial factoring to 729514
1044787004...5985897087 has no small factor.
[Elapsed time: 0.999 seconds]
modified2013-02-16 12:06:20
created2013-02-16 06:48:01
id152779

fieldvalue
prime_id111254
person_id9
machineDitto P4 P4
whatprp
notesPFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing 1044787004...5985897087 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N+1 BLS with factored part 0.14% and helper 0.01% (0.43% proof)
1044787004...5985897087 is Fermat and Lucas PRP! (3.1798s+0.0008s)
[Elapsed time: 3.00 seconds]
modified2013-02-16 07:23:17
created2013-02-16 07:23:14
id152784

Query times: 0.0006 seconds to select prime, 0.0007 seconds to seek comments.