Phi(3, - 69165016384)
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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

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, - 69165016384)
Verification status (*):Proven
Official Comment:Generalized unique
Proof-code(s): (*):f1 : Chaglassian, PhiSieve, PIES, ForEis
Decimal Digits:191362   (log10 is 191361.396941622)
Rank (*):28168 (digit rank is 1)
Entrance Rank (*):193
Currently on list? (*):no
Submitted:4/7/2005 19:21:12 CDT
Last modified:4/7/2005 19:21:12 CDT
Database id:74029
Status Flags:none
Score (*):41.5524 (normalized score 0.0795)

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 262
Subcategory: "Generalized Unique"
(archival tag id 209119, 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.
machineLinux P4 2.8GHz
notesCommand: /home/caldwell/client/pfgw -f -t -q"Phi(3,-691650^16384)" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing Phi(3,-691650^16384) [N-1, Brillhart-Lehmer-Selfridge]
trial factoring to 68119460
Running N-1 test using base 11
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(81920,20) to FFT(81920,19)
Reduced from FFT(81920,19) to FFT(81920,18)
Reduced from FFT(81920,18) to FFT(81920,17)
Reduced from FFT(81920,17) to FFT(81920,16)
1271386 bit request FFT size=(81920,16)
Calling Brillhart-Lehmer-Selfridge with factored part 39.25%
Phi(3,-691650^16384) is prime! (-1285.4946s+0.2900s)
modified2005-04-18 11:33:10
created2005-04-07 19:23:00

Query times: 0.0005 seconds to select prime, 0.0004 seconds to seek comments.