289 · 2989182 + 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:289 · 2989182 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L1446 : Harvey, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:297776   (log10 is 297775.91406873)
Rank (*):16443 (digit rank is 1)
Entrance Rank (*):446
Currently on list? (*):no
Submitted:10/25/2010 10:26:42 CDT
Last modified:10/25/2010 12:20:20 CDT
Removed (*):8/4/2013 14:33:37 CDT
Database id:95676
Status Flags:none
Score (*):42.9124 (normalized score 0.2682)

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.
Generalized Fermat (archivable *)
Prime on list: no, rank 1431
Subcategory: "Generalized Fermat"
(archival tag id 210866, tag last modified 2020-09-20 14:50:24)

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.

Steven Harvey writes (11 Sep 2014):  (report abuse)
289*2^989182+1 is a Factor of xGF(989181,3,2)

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_id95676
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -t -q"289*2^989182+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 289*2^989182+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(131072,20) to FFT(131072,19) Reduced from FFT(131072,19) to FFT(131072,18) Reduced from FFT(131072,18) to FFT(131072,17) Reduced from FFT(131072,17) to FFT(131072,16) 1978390 bit request FFT size=(131072,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 289*2^989182+1 is prime! (5939.3984s+0.0008s) [Elapsed time: 1.65 hours]
modified2020-07-07 17:30:33
created2010-10-25 10:33:36
id120738

fieldvalue
prime_id95676
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 289 2 989182 1 2>&1 [Elapsed time: 10.362 seconds]
modified2020-07-07 17:30:33
created2010-10-25 10:35:02
id120739

Query times: 0.001 seconds to select prime, 0.0007 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.