Phi(3, - 183372616384)

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.

Description:Phi(3, - 183372616384)
Verification status (*):Proven
Official Comment (*):Generalized unique
Proof-code(s): (*):f6 : Carmody, PhiSieve, PIES, ForEis
Decimal Digits:205237   (log10 is 205236.94302155)
Rank (*):24533 (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 0.0852)

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 173
Subcategory: "Generalized Unique"
(archival tag id 224249, tag last modified 2020-08-04 13:50:04)

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,-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]
modified2020-07-07 17:30:42
created2006-10-11 14:52:02

machineRedHat P4 P4
notesCommand: /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) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 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 Brillhart-Lehmer-Selfridge with factored part 43.79% Phi(3,-1833726^16384) is prime! (-698.6046s+0.2900s) [Elapsed time: 8183 seconds]
modified2020-07-07 17:30:42
created2006-10-11 14:53:01

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
Printed from the PrimePages <> © Chris Caldwell.