Phi(3, - 123447524288)
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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, - 123447524288)
Verification status (*):Proven
Official Comment:Generalized unique
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L4561 : Propper, Batalov, CycloSv, Cyclo, EMsieve, PIES, LLR
Decimal Digits:5338805   (log10 is 5338804.29892426)
Rank (*):17 (digit rank is 1)
Entrance Rank (*):12
Currently on list? (*):short
Submitted:2/23/2017 02:04:25 CDT
Last modified:3/8/2017 09:05:55 CDT
Database id:123041
Status Flags:TrialDiv
Score (*):51.7663 (normalized score 2295.5242)

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: yes, rank 1
Subcategory: "Generalized Unique"
(archival tag id 218652, tag last modified 2017-03-06 16:20:05)

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.

Serge Batalov writes (23 Feb 2017): 
Starting N-1 prime test of 123447^1048576-123447^524288+1
Using generic reduction FMA3 FFT length 1920K, Pass1=320, Pass2=6K, 16 threads, a = 7
123447^1048576-123447^524288+1 may be prime, trying to compute gcd's
7^((N-1)/41149)-1 is coprime to N!
7^((N-1)/3)-1 is coprime to N!
123447^1048576-123447^524288+1 is prime! (5338805 decimal digits)  Time : 187808.030 sec.

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.
machineUsing: Xeon (pool) 4c+4c 3.5GHz
notesCommand: /home/caldwell/clientpool/1/pfgw64 -t -q"Phi(3,-123447^524288)" 2>&1
PFGW Version [GWNUM 27.11]
Primality testing Phi(3,-123447^524288) [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Calling Brillhart-Lehmer-Selfridge with factored part 45.31%

Phi(3,-123447^524288) is prime! (1147972.7831s+0.6828s)
[Elapsed time: 13.29 days]
modified2017-03-31 15:53:56
created2017-02-23 02:13:01

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