4658592097152 - 4658591048576 + 1

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:4658592097152 - 4658591048576 + 1
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:11887192   (log10 is 11887191.240435)
Rank (*):8 (digit rank is 1)
Entrance Rank (*):7
Currently on list? (*):short
Submitted:5/31/2023 19:32:31 UTC
Last modified:7/25/2023 13:37:29 UTC
Database id:136107
Status Flags:none
Score (*):54.2155 (normalized score 9964.87)

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 2
Subcategory: "Generalized Unique"
(archival tag id 228727, tag last modified 2023-12-14 08:37:23)

User comments about this prime (disclaimer):

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Serge Batalov writes (1 Jun 2023):  (report abuse)
Also can be written as:
465859^2097152-465859^1048576+1 = (465859^1048576-1)*465859^1048576+1
to demonstrate that Pocklington N-1 primality test as implemented in LLR is applicable.

N-1 proof with LLR is performed externally (using multiple a values, and on different hardware). For additional validation and to avoid software bias, PRP tests are adding different s/w (Prime95) using mulitple bases . Finally, Cyclo gproof is available (though this is yet not a widely recognized format).

Starting N-1 prime test of 465859^2097152-465859^1048576+1
Base factorized as : 199*2341
Base prime factor(s) taken : 199, 2341
Input matches Phi(3,-465859^1048576) - all-complex FFT length 3*2^20 is applicable. 
Using all-complex AVX-512 FFT length 3M, Pass1=192, Pass2=16K, clm=4, 24 threads, a = 11
465859^2097152-465859^1048576+1 may be prime, trying to compute gcd's
11^((N-1)/2341)-1 is coprime to N!
11^((N-1)/199)-1 is coprime to N!
465859^2097152-465859^1048576+1 is prime! (11887192 decimal digits)  Time : 49687.570 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_id136107
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesCommand: /var/www/clientpool/1/pfgw64 -V -f -t -q"Phi(3,-465859^1048576)" 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing Phi(3,-465859^1048576) [N-1, Brillhart-Lehmer-Selfridge]
trial


Running N-1 test using base 7
Generic modular reduction using generic reduction AVX-512 FFT length 4200K, Pass1=1920, Pass2=2240, clm=1 on A 39488395-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 50.00%


Phi(3,-465859^1048576) is prime! (4730339.7767s+1.8951s)
[Elapsed time: 54.75 days]
modified2023-07-25 13:32:04
created2023-05-31 19:33:01
id181937

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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