# Phi(3, - 123447524288)

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.

#### This prime's information:

Description: Phi(3, - 123447524288) Proven Generalized unique This prime has 1 user comment below. L4561 : Propper, Batalov, CycloSv, Cyclo, EMsieve, PIES, LLR 5338805   (log10 is 5338804.2989243) 27 (digit rank is 1) 12 short 2/23/2017 08:04:25 UTC 3/11/2023 15:54:10 UTC 123041 TrialDiv 51.7663 (normalized score 1096.7956)

#### 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"

Serge Batalov writes (23 Feb 2017):  (report abuse)
 ```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.
fieldvalue
prime_id123041
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/clientpool/1/pfgw64 -t -q"Phi(3,-123447^524288)" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [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]
modified2020-07-07 22:30:16
created2017-02-23 08:13:01
id168686

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.