Phi(3, 9425959049)

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, 9425959049)
Verification status (*):Proven
Official Comment (*):Generalized unique
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p269 : Zhou, OpenPFGW
Decimal Digits:587458   (log10 is 587457.57733985)
Rank (*):2864 (digit rank is 1)
Entrance Rank (*):537
Currently on list? (*):yes
Submitted:7/4/2014 07:29:54 CDT
Last modified:7/4/2014 15:50:04 CDT
Database id:118125
Status Flags:TrialDiv
Score (*):45.0001 (normalized score 1.7402)

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 54
Subcategory: "Generalized Unique"
(archival tag id 224130, tag last modified 2020-08-04 13:50:04)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

Lei Zhou writes (11 Sep 2014):  (report abuse)
This number is Phi(3^11, 94259) = 1+94259^(3^10)+94259^(2*3^10). Such numbers are listed in OEIS A153438.

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.
machineXeon 4c+4c 3.5GHz
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"94259^59049+94259^118098+1" 2>&1 PFGW Version [GWNUM 27.11] Primality testing 94259^59049+94259^118098+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Calling Brillhart-Lehmer-Selfridge with factored part 37.15% 94259^59049+94259^118098+1 is prime! (7106.4866s+0.0246s) [Elapsed time: 1.97 hours]
modified2020-07-07 17:30:17
created2014-07-04 07:31:22

Query times: 0.0007 seconds to select prime, 0.0008 seconds to seek comments.
Printed from the PrimePages <> © Chris Caldwell.