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: 81 · 21643428+1 Verification status (*): Proven Official Comment: Generalized Fermat Proof-code(s): (*): g418 : Taura, PRP, NewPGen, Proth.exe Decimal Digits: 494724   (log10 is 494723.03219909) Rank (*): 97 (digit rank is 1) Entrance Rank (*): 88 Currently on list? (*): short Submitted: 3/6/2009 17:53:42 CDT Last modified: 3/6/2009 23:50:20 CDT Database id: 87009 Status Flags: none Score (*): 44.4725 (normalized score 47.2693)

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: yes, rank 9
Subcategory: "Generalized Fermat"
(archival tag id 208929, tag last modified 2009-10-16 03:20:21)

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.

field value prime_id 87009 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/TrialDiv/TrialDiv -q 81 2 1643428 1 2>&1 [Ellapsed time: 10.077 seconds] modified 2009-03-24 13:31:30 created 2009-03-06 18:05:01 id 103387

field value prime_id 87009 person_id 9 machine Ditto P4 P4 what prime notes Command: /home/ditto/client/pfgw -t -q"81*2^1643428+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 81*2^1643428+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(229376,19) to FFT(229376,18) Reduced from FFT(229376,18) to FFT(229376,17) Reduced from FFT(229376,17) to FFT(229376,16) 3286878 bit request FFT size=(229376,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 81*2^1643428+1 is prime! (19425.1235s+0.0014s) [Elapsed time: 5.40 hours] modified 2009-03-24 13:31:30 created 2009-03-06 18:08:02 id 103388