25 · 22141884 + 1
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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:25 · 22141884 + 1
Verification status (*):Proven
Official Comment:Divides Fermat F(2141872), GF(2141871,5), GF(2141872,10); generalized Fermat
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L1741 : Granowski, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:644773   (log10 is 644772.72917276)
Rank (*):987 (digit rank is 1)
Entrance Rank (*):88
Currently on list? (*):short
Submitted:9/12/2011 09:15:05 CDT
Last modified:9/18/2011 16:02:01 CDT
Database id:101943
Status Flags:none
Score (*):45.286 (normalized score 4.613)

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.
Fermat Divisors (archivable *)
Prime on list: yes, rank 8, weight 48.504926878193
Subcategory: "Divides Fermat"
(archival tag id 213460, tag last modified 2016-03-15 13:57:14)
Generalized Fermat (archivable *)
Prime on list: no, rank 120
Subcategory: "Generalized Fermat"
(archival tag id 213461, tag last modified 2017-12-04 03:50:21)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 7, weight 48.504926878193
Subcategory: "Divides GF(*,5)"
(archival tag id 213462, tag last modified 2016-03-15 13:57:15)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 6, weight 48.504926878193
Subcategory: "Divides GF(*,10)"
(archival tag id 213463, tag last modified 2017-08-24 21:20:02)

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.

PrimeGrid writes (11 Sep 2014): 
25*2^2141884+1 Divides Fermat F(2141872)
25*2^2141884+1 Divides GF(2141871,5)
25*2^2141884+1 Divides xGF(2141872,5,2)
25*2^2141884+1 Divides xGF(2141867,5,4)
25*2^2141884+1 Divides xGF(2141872,8,5)
25*2^2141884+1 Divides GF(2141872,10)

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_id101943
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 25 2 2141884 1 2>&1
[Elapsed time: 10.842 seconds]
modified2011-12-27 16:48:29
created2011-09-12 09:18:02
id133452

fieldvalue
prime_id101943
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"25*2^2141884+1" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing 25*2^2141884+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
25*2^2141884+1 is prime! (9202.9641s+0.0015s)
[Elapsed time: 2.56 hours]
modified2011-12-27 16:48:29
created2011-09-12 09:23:01
id133453

Query times: 0.0004 seconds to select prime, 0.0008 seconds to seek comments.