
The nth Prime Page will now find any of the first 2,623,557,157,654,233 primes or
π( x) for x up to 100,000,000,000,000,000.
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,  2322573^{16384}) 
Verification status (*):  Proven 
Official Comment:  Generalized unique 
Proofcode(s): (*):  p72 : Caldwell, ForEis, PhiSieve, PIES, OpenPFGW 
Decimal Digits:  208601 (log_{10} is 208600.08441584) 
Rank (*):  19845 (digit rank is 1) 
Entrance Rank (*):  468 
Currently on list? (*):  no 
Submitted:  1/17/2008 15:10:06 CDT 
Last modified:  1/17/2008 18:59:37 CDT 
Database id:  83711 
Status Flags:  none 
Score (*):  41.8178 (normalized score 0.1479) 

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 114
Subcategory: "Generalized Unique"
(archival tag id 209003, tag last modified 20170121 15:20:15)
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  83711 
person_id  9 
machine  RedHat P4 P4 
what  trial_divided 
notes  Command: /home/caldwell/client/pfgw o f1{98304} q"Phi(3,2322573^16384)" 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 14024224057 Phi(3,2322573^16384) has no small factor. [Elapsed time: 18.598 seconds]

modified  20111227 16:48:48 
created  20080117 15:22:11 
id  96552 

field  value 
prime_id  83711 
person_id  9 
machine  RedHat P4 P4 
what  prime 
notes  Command: /home/caldwell/client/pfgw t q"Phi(3,2322573^16384)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing Phi(3,2322573^16384) [N1, BrillhartLehmerSelfridge] Running N1 test using base 13 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) 1385918 bit request FFT size=(98304,16) Calling BrillhartLehmerSelfridge with factored part 38.07% Phi(3,2322573^16384) is prime! (11423.9279s+0.8275s) [Elapsed time: 3.17 hours]

modified  20080120 07:55:05 
created  20080117 15:49:12 
id  96556 

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