833000864 · 3011# + 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:833000864 · 3011# + 1
Verification status (*):Proven
Official Comment (*):Arithmetic progression (7,d=114858412*3011#)
Proof-code(s): (*):p155 : DavisK, NewPGen, OpenPFGW
Decimal Digits:1290   (log10 is 1289.38404688)
Rank (*):113730 (digit rank is 14)
Entrance Rank (*):56933
Currently on list? (*):no
Submitted:2/18/2006 07:29:24 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:77093
Status Flags:none
Score (*):26.0667 (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 452, weight 45.873813539619
Subcategory: "Arithmetic progression (7,d=*)"
(archival tag id 184738, 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_id77093
person_id9
machineLinux P4 2.8GHz
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 833000864 3011 # 1 2>&1 [Elapsed time: 244.633 seconds]
modified2020-07-07 22:30:42
created2006-02-18 07:52:01
id83167

fieldvalue
prime_id77093
person_id9
machineLinux P4 2.8GHz
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"833000864*3011#+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 833000864*3011#+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3019 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(512,22) to FFT(512,21) Reduced from FFT(512,21) to FFT(512,20) Reduced from FFT(512,20) to FFT(512,19) Reduced from FFT(512,19) to FFT(512,18) Reduced from FFT(512,18) to FFT(512,17) 8576 bit request FFT size=(512,17) Calling Brillhart-Lehmer-Selfridge with factored part 33.50% 833000864*3011#+1 is prime! (4.1562s+0.0733s) [Elapsed time: 5 seconds]
modified2020-07-07 22:30:42
created2006-02-18 07:53:02
id83168

Query times: 0.0003 seconds to select prime, 0.0003 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.