(20431926447260679 · 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:(20431926447260679 · 4001# · (205881 · 4001# + 1) + 210) · (205881 · 4001# - 1)/35 + 1
Verification status (*):Proven
Official Comment (*):Triplet (1)
Proof-code(s): (*):p179 : DavisK, APTreeSieve, OpenPFGW
Decimal Digits:5132   (log10 is 5131.96657434)
Rank (*):90767 (digit rank is 3)
Entrance Rank (*):38188
Currently on list? (*):no
Submitted:3/10/2006 05:49:40 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:77266
Status Flags:none
Score (*):30.3701 (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.
Triplet (archivable class *)
Prime on list: no, rank 33
Subcategory: "Triplet (1)"
(archival tag id 195093, 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.
fieldvalue
prime_id77266
person_id9
machineLinux P4 2.8GHz
whattrial_divided
notesCommand: /home/caldwell/client/pfgw -o -f -q"(99241437759*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] (99241437759*205881*4001#.........10)*(205881*4001 1/1 trial factoring to 1395014 (99241437759*205881*4001#*(205881*4001#+1)+210)*(205881*4001#-1)/35+1 has no small factor. [Elapsed time: 0.683 seconds]
modified2020-07-07 22:30:42
created2006-03-10 05:52:00
id83530

fieldvalue
prime_id77266
person_id9
machineLinux P4 2.8GHz
whatprime
notesPFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (99241437759*205881*4001#*(205881*4001#+1)+210)*(205881*4001#-1)/35+1 [N-1, Brillhart-Lehmer-Selfridge] Reading factors from helper file helper.txt Running N-1 test using base 2 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF 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) 34106 bit request FFT size=(2048,17) Calling Brillhart-Lehmer-Selfridge with factored part 33.28% 1/44304212 (99241437759*205881*4001#*(205881*4001#+1)+210)*(205881*4001#-1)/35+1 is prime! (9569.2795s+0.0016s) [Elapsed time: 9570 seconds] Helper File: 205881*4001#-1 205881*4001#+1
modified2020-07-07 22:30:42
created2006-03-10 14:11:45
id83557

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