4 · 511786358 + 1

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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.

This prime's information:

Description:4 · 511786358 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):A2 : Propper, Srsieve, PRST
Decimal Digits:8238312   (log10 is 8238311.3044259)
Rank (*):14 (digit rank is 1)
Entrance Rank (*):13
Currently on list? (*):yes
Submitted:10/1/2024 03:13:57 UTC
Last modified:10/4/2024 15:37:10 UTC
Database id:138596
Status Flags:none
Score (*):53.0939 (normalized score 2807.3477)

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 Fermat (archivable *)
Prime on list: yes, rank 1
Subcategory: "Generalized Fermat"
(archival tag id 229673, tag last modified 2024-10-04 15:37:11)

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.

Ryan Propper writes (1 Oct 2024):  (report abuse) 
$ ./prst_13.1  -check strong -t 18 -log info "4*5^11786358+1"
Using negacyclic AVX-512 FFT length 1600K, Pass1=1K, Pass2=1600, clm=2, 18 threads.
Pocklington test of 4*5^11786358+1, a = 3, complexity = 27420488.
4*5^11786358+1 Gerbicz-Li check enabled, L2 = 1402*1220.
4*5^11786358+1 is a probable prime. Time: 16397.8 s.
4*5^11786358+1 Checking gcd with factors {2}.
Restarting Pocklington test of 4*5^11786358+1, a = 5.
4*5^11786358+1 Gerbicz-Li check enabled, L2 = 1402*1220.
4*5^11786358+1 is a probable prime. Time: 32590.5 s.
4*5^11786358+1 Checking gcd with factors {5}.
4*5^11786358+1 is prime!

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_id138596
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesCommand: /var/www/clientpool/1/pfgw64 -V -f -t -q"4*5^11786358+1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 4*5^11786358+1 [N-1, Brillhart-Lehmer-Selfridge]
trial


Running N-1 test using base 2
Special modular reduction using all-complex AVX-512 FFT length 1600K, Pass1=1K, Pass2=1600, clm=2 on 4*5^11786358+1
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%


4*5^11786358+1 is prime! (302767.2447s+0.1200s)
[Elapsed time: 3.50 days]
modified2024-10-04 15:20:14
created2024-10-01 03:14:02
id184440

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