10999 + 7

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:10999 + 7
Verification status (*):PRP
Official Comment (*):Smallest titanic, cyclotomy
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):PM : Mihailescu
Decimal Digits:1000   (log10 is 999)
Rank (*):132578 (digit rank is 55)
Entrance Rank (*):35158
Currently on list? (*):no
Submitted:4/1/1998 05:59:59 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:58901
Status Flags:Verify
Score (*):25.2688 (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.
Cyclotomy Proof (tolerated *)
Prime on list: no, rank 128
Subcategory: "Cyclotomy Proof"
(archival tag id 178120, tag last modified 2023-03-11 15:53:59)
* old special cases (deprecated *)
Prime on list: no, rank 3
Subcategory: "* old special cases"
(archival tag id 178119, tag last modified 2023-03-11 15:53:59)

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.

Jeppe Stig Nielsen writes (31 Jan 2022):  (report abuse)
Primality certificate available at factordb.com.

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_id58901
person_id9
machineLinux PII 200
whatprp
notesPFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') 10^999+7 is 3-PRP! (1.430000 seconds)
modified2003-03-25 17:23:05
created2003-01-04 05:05:29
id60245

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