Phi(3, - 123447⁵²⁴²⁸⁸)

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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, - 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 5338804.2989243)
Rank (*):	23 (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 1305.3438)

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 224077, 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.
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.

field value

prime_id 123041

person_id 9

machine Using: Xeon (pool) 4c+4c 3.5GHz

what prime

notes Command: /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]

modified 2020-07-07 17:30:16

created 2017-02-23 02:13:01

id 168686

field	value
prime_id	123041
person_id	9
machine	Using: Xeon (pool) 4c+4c 3.5GHz
what	prime
notes	Command: /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]
modified	2020-07-07 17:30:16
created	2017-02-23 02:13:01
id	168686

Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.

Phi(3, - 123447524288)

Archival tags:

User comments about this prime (disclaimer):

Verification data:

Phi(3, - 123447⁵²⁴²⁸⁸)