(1049713153083 · 2917# · (567 · 2917# + 1) + 2310) · (567 · 2917# - 1)/210 + 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:(1049713153083 · 2917# · (567 · 2917# + 1) + 2310) · (567 · 2917# - 1)/210 + 1
Verification status (*):PRP
Official Comment (*):Quadruplet (1),ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c101 : DavisK, APTreeSieve, OpenPFGW, Primo
Decimal Digits:3753   (log10 is 3752.4184173535)
Rank (*):94175 (digit rank is 4)
Entrance Rank (*):92279
Currently on list? (*):short
Submitted:7/22/2023 08:00:28 UTC
Last modified:7/30/2023 17:37:05 UTC
Database id:136279
Status Flags:Verify
Score (*):29.3968 (normalized score 0)

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.
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 669
Subcategory: "ECPP"
(archival tag id 228736, tag last modified 2024-04-24 05:37:26)
Quadruplet (archivable class *)
Prime on list: yes, rank 3
Subcategory: "Quadruplet (1)"
(archival tag id 228737, tag last modified 2023-07-30 17:37:12)

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.

Jeppe Stig Nielsen writes (24 Jul 2023):  (report abuse)
Apparently needs ECPP since N-1 is not sufficiently factored. Finder uploaded certificate at factordb.com/index.php?id=1100000004682544884.

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 -f -t -q"(1049713153083*2917#*(567*2917#+1)+2310)*(567*2917#-1)/210+1" 2>&1
PFGW Version [GWNUM 30.11]
Primality testing (1049713153083*2917#*(567*2917#+1)+2310)*(567*2917#-1)/210+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 7
Generic modular reduction using generic reduction FMA3 FFT length 1280 on A 12466-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.08%

(1049713153083*2917#*(567*2917#+1)+2310)*(567*2917#-1)/210+1 is PRP! (0.6535s+0.0065s)
[Elapsed time: 1.00 seconds]
modified2023-07-22 12:22:03
created2023-07-22 12:22:02

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