340155919 · 3301# + 1
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At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: 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:

field (help)value
Description:340155919 · 3301# + 1
Verification status (*):Proven
Official Comment:Arithmetic progression (3,d=30017636*3301#)
Proof-code(s): (*):p252 : Oakes, NewPGen, OpenPFGW
Decimal Digits:1401   (log10 is 1400.9721120224)
Rank (*):96803 (digit rank is 1)
Entrance Rank (*):70317
Currently on list? (*):no
Submitted:8/15/2010 04:13:29 CDT
Last modified:8/15/2010 04:50:31 CDT
Database id:94183
Status Flags:none
Score (*):26.3261 (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 327, weight 30.9198104585031
Subcategory: "Arithmetic progression (3,d=*)"
(archival tag id 210818, tag last modified 2017-08-19 13:50:02)

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_id94183
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 340155919 3301 # 1 2>&1
[Elapsed time: 188.849 seconds]
modified2011-12-27 16:48:38
created2010-08-15 04:31:11
id117754

fieldvalue
prime_id94183
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"340155919*3301#+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 340155919*3301#+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
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)
9316 bit request FFT size=(512,19)
Running N-1 test using base 7
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)
9316 bit request FFT size=(512,19)
Calling Brillhart-Lehmer-Selfridge with factored part 33.46%
340155919*3301#+1 is prime! (2.1665s+0.0007s)
[Elapsed time: 2.00 seconds]
modified2010-10-13 12:41:35
created2010-08-15 04:23:11
id117748

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.