(84055657369 · 205881 · 4001# · (205881 · 4001# + 1) + 210) · (205881 · 4001# - 1)/35 + 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:(84055657369 · 205881 · 4001# · (205881 · 4001# + 1) + 210) · (205881 · 4001# - 1)/35 + 1
Verification status (*):Proven
Official Comment (*):Consecutive primes arithmetic progression (1,d=6)
Proof-code(s): (*):p179 : DavisK, APTreeSieve, OpenPFGW
Decimal Digits:5132   (log10 is 5131.89444824)
Rank (*):89315 (digit rank is 9)
Entrance Rank (*):38380
Currently on list? (*):no
Submitted:4/1/2006 12:26:30 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:77460
Status Flags:none
Score (*):30.37 (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.
Arithmetic Progressions of Primes (archivable class *)
Prime on list: no, rank 294
Subcategory: "Arithmetic progression (1,d=*)"
(archival tag id 195102, tag last modified 2023-03-11 15:53:59)
Consecutive Primes in Arithmetic Progression (archivable class *)
Prime on list: no, rank 20
Subcategory: "Consecutive primes in arithmetic progression (1,d=*)"
(archival tag id 195101, tag last modified 2023-03-11 15:53:59)

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.
machineGenToo P3 400MHz
notesPFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (84055657369*205881*4001#*(205881*4001#+1)+210)*(205881*4001#-1)/35+1 [N-1, Brillhart-Lehmer-Selfridge] Reading factors from helper file helper_file_id_77460 Running N-1 test using base 5 Using non-SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(2048,22) to FFT(2048,21) Reduced from FFT(2048,21) to FFT(2048,20) Reduced from FFT(2048,20) to FFT(2048,19) Reduced from FFT(2048,19) to FFT(2048,18) Reduced from FFT(2048,18) to FFT(2048,17) 34104 bit request FFT size=(2048,17) Calling Brillhart-Lehmer-Selfridge with factored part 33.34% (84055657369*205881*4001#*(205881*4001#+1)+210)*(205881*4001#-1)/35+1 is prime! (34.7000s+0.0100s) [Elapsed time: 36 seconds] Helper file contains: "205881*4001#-1"
modified2020-07-07 22:30:42
created2006-04-04 13:24:53

machineGenToo P3 400MHz
notesCommand: /home/caldwell/client/pfgw -o -f -q"(84055657369*205881*4001#*(205881*4001#+1)+210)*(205881*4001#-1)/35+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] (84055657369*205881*4001#.........10)*(205881*4001 1/1 trial factoring to 1394925 (84055657369*205881*4001#*(205881*4001#+1)+210)*(205881*4001#-1)/35+1 has no small factor. [Elapsed time: 0.716 seconds]
modified2020-07-07 22:30:42
created2006-07-07 15:40:35

Query times: 0.0002 seconds to select prime, 0.0005 seconds to seek comments.
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