Phi(3, - 232257316384)
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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, - 232257316384)
Verification status (*):Proven
Official Comment:Generalized unique
Proof-code(s): (*):p72 : Caldwell, ForEis, PhiSieve, PIES, OpenPFGW
Decimal Digits:208601   (log10 is 208600.08441584)
Rank (*):21476 (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 0.1327)

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 145
Subcategory: "Generalized Unique"
(archival tag id 209003, tag last modified 2017-11-01 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.
machineRedHat P4 P4
notesCommand: /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]
modified2011-12-27 16:48:48
created2008-01-17 15:22:11

machineRedHat P4 P4
notesCommand: /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) [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 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 Brillhart-Lehmer-Selfridge with factored part 38.07%
Phi(3,-2322573^16384) is prime! (11423.9279s+0.8275s)
[Elapsed time: 3.17 hours]
modified2008-01-20 07:55:05
created2008-01-17 15:49:12

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.