228188131072 + 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.

This prime's information:

Description:228188131072 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Proof-code(s): (*):g124 : Crickman, Proth.exe
Decimal Digits:702323   (log10 is 702322.154132)
Rank (*):3578 (digit rank is 1)
Entrance Rank (*):56
Currently on list? (*):yes
Submitted:8/20/2010 00:25:08 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:94353
Status Flags:none
Score (*):45.5485 (normalized score 2.0947)

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 1018
Subcategory: "Generalized Fermat"
(archival tag id 210831, tag last modified 2023-09-24 13:37:27)

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.
machineDitto P4 P4
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 1 228188 131072 1 2>&1 [Elapsed time: 8.063 seconds]
modified2020-07-07 22:30:33
created2010-08-20 00:35:01

machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -t -q"228188^131072+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 228188^131072+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(327680,19) to FFT(327680,18) Reduced from FFT(327680,18) to FFT(327680,17) Reduced from FFT(327680,17) to FFT(327680,16) 4666136 bit request FFT size=(327680,16) Calling Brillhart-Lehmer-Selfridge with factored part 88.76% 228188^131072+1 is prime! (99736.9294s+0.1414s) [Elapsed time: 27.70 hours]
modified2020-07-07 22:30:33
created2010-08-20 00:38:02

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