
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:  Phi(3,  1833726^{16384}) 
Verification status (*):  Proven 
Official Comment:  Generalized unique 
Proofcode(s): (*):  f6 : Carmody, PhiSieve, PIES, ForEis 
Decimal Digits:  205237 (log_{10} is 205236.94302155) 
Rank (*):  23253 (digit rank is 1) 
Entrance Rank (*):  296 
Currently on list? (*):  no 
Submitted:  10/11/2006 14:29:01 CDT 
Last modified:  10/11/2006 17:09:24 CDT 
Database id:  78645 
Status Flags:  none 
Score (*):  41.7678 (normalized score 0.1032) 

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 Unique (archivable *)
 Prime on list: no, rank 167
Subcategory: "Generalized Unique"
(archival tag id 209025, tag last modified 20171101 02:50:22)
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  78645 
person_id  9 
machine  RedHat P4 P4 
what  trial_divided 
notes  Command: /home/caldwell/client/pfgw o f1{98304} q"Phi(3,1833726^16384)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Factoring numbers to 1% of normal. Using modular factorization: {98304} trial factoring to 13814264571 Phi(3,1833726^16384) has no small factor. [Elapsed time: 17.426 seconds]

modified  20070303 21:00:43 
created  20061011 14:52:02 
id  86387 

field  value 
prime_id  78645 
person_id  9 
machine  RedHat P4 P4 
what  prime 
notes  Command: /home/caldwell/client/pfgw t q"Phi(3,1833726^16384)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing Phi(3,1833726^16384) [N1, BrillhartLehmerSelfridge] Running N1 test using base 11 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(98304,20) to FFT(98304,19) Reduced from FFT(98304,19) to FFT(98304,18) Reduced from FFT(98304,18) to FFT(98304,17) Reduced from FFT(98304,17) to FFT(98304,16) 1363574 bit request FFT size=(98304,16) Calling BrillhartLehmerSelfridge with factored part 43.79% Phi(3,1833726^16384) is prime! (698.6046s+0.2900s) [Elapsed time: 8183 seconds]

modified  20070303 21:00:43 
created  20061011 14:53:01 
id  86388 

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.
