289 · 2252858 + 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 · 2252858 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Proof-code(s): (*):p43 : Fougeron, OpenPFGW
Decimal Digits:76121   (log10 is 76120.303541446)
Rank (*):49463 (digit rank is 1)
Entrance Rank (*):1661
Currently on list? (*):no
Submitted:2/20/2005 07:58:54 CDT
Last modified:2/20/2005 07:58:54 CDT
Removed (*):11/20/2006 10:39:27 CDT
Database id:73492
Status Flags:none
Score (*):38.7133 (normalized score 0.0032)

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 2641
Subcategory: "Generalized Fermat"
(archival tag id 205221, tag last modified 2021-12-03 20:37:45)

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_id73492
person_id9
machineLinux P4 2.8GHz
whatprime
notesCommand: /home/caldwell/client/pfgw -f -t -q"289*2^252858+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 289*2^252858+1 [N-1, Brillhart-Lehmer-Selfridge] trial factoring to 25465056 Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(32768,20) to FFT(32768,19) Reduced from FFT(32768,19) to FFT(32768,18) Reduced from FFT(32768,18) to FFT(32768,17) Reduced from FFT(32768,17) to FFT(32768,16) 505742 bit request FFT size=(32768,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 289*2^252858+1 is prime! (2450.7585s+0.0444s)
modified2020-07-07 17:30:44
created2005-02-20 08:23:01
id78508

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