# 25 · 22141884 + 1

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.

Description: 25 · 22141884 + 1 Proven Divides Fermat F(2141872), GF(2141871,5), GF(2141872,10); generalized Fermat This prime has 1 user comment below. L1741 : Granowski, PSieve, Srsieve, PrimeGrid, LLR 644773   (log10 is 644772.72917276) 1840 (digit rank is 1) 88 short 9/12/2011 09:15:05 CDT 9/18/2011 16:02:01 CDT 101943 none 45.286 (normalized score 2.885)

#### 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 9, weight 48.504926878193
Subcategory: "Divides Fermat"
Generalized Fermat (archivable *)
Prime on list: no, rank 363
Subcategory: "Generalized Fermat"
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 11, weight 48.504926878193
Subcategory: "Divides GF(*,5)"
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 6, weight 48.504926878193
Subcategory: "Divides GF(*,10)"

PrimeGrid writes (11 Sep 2014):  (report abuse)
 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]
modified2020-07-07 17:30:30
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]
modified2020-07-07 17:30:30
created2011-09-12 09:23:01
id133453

Query times: 0.0008 seconds to select prime, 0.0003 seconds to seek comments.