69 · 27452023 + 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:69 · 27452023 + 1
Verification status (*):Proven
Official Comment (*):Divides GF(7452020,3) [GG]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L4965 : Propper, LLR
Decimal Digits:2243285   (log10 is 2243284.290227)
Rank (*):214 (digit rank is 1)
Entrance Rank (*):168
Currently on list? (*):short
Submitted:3/23/2023 14:26:42 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:135837
Status Flags:none
Score (*):49.1105 (normalized score 59.6959)

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 Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 5, weight 53.344651780459
Subcategory: "Divides GF(*,3)"
(archival tag id 228435, tag last modified 2023-03-31 00:37:47)

User comments about this prime (disclaimer):

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Gary B. Gostin writes (24 Mar 2023):  (report abuse)
Divides GF(7452020,3)

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: Digital Ocean Droplet
notesCommand: /var/www/clientpool/1/pfgw64 -V -t -q"69*2^7452023+1" 2>&1
PFGW Version [GWNUM 30.11]
Primality testing 69*2^7452023+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Special modular reduction using all-complex AVX-512 FFT length 448K, Pass1=1K, Pass2=448, clm=1 on 69*2^7452023+1
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%

69*2^7452023+1 is prime! (15622.4269s+0.0031s)
[Elapsed time: 4.34 hours]
modified2023-03-24 08:54:11
created2023-03-24 04:33:48

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