21667321 - 2833661 + 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:21667321 - 2833661 + 1
Verification status (*):Proven
Official Comment:Gaussian Mersenne norm 38?
Proof-code(s): (*):L137 : Jaworski, Rieselprime, LLR
Decimal Digits:501914   (log10 is 501913.63340047)
Rank (*):2076 (digit rank is 1)
Entrance Rank (*):109
Currently on list? (*):short
Submitted:1/14/2011 01:06:44 CDT
Last modified:1/14/2011 17:20:22 CDT
Database id:97416
Status Flags:none
Score (*):44.5168 (normalized score 1.9262)

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.
Gaussian Mersenne norm (archivable *)
Prime on list: yes, rank 3
Subcategory: "Gaussian Mersenne norm"
(archival tag id 213060, tag last modified 2014-09-06 19:20:24)

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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -o -f -q"2^1667321-2^833661+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
trial factoring to 189921883
2^1667321-2^833661+1 has no small factor.
[Elapsed time: 6036.135 seconds]
modified2011-12-27 16:48:35
created2011-01-14 01:18:02

machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -t -q"2^1667321-2^833661+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 2^1667321-2^833661+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 13
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(229376,19) to FFT(229376,18)
Reduced from FFT(229376,18) to FFT(229376,17)
Reduced from FFT(229376,17) to FFT(229376,16)
3334650 bit request FFT size=(229376,16)
Calling Brillhart-Lehmer-Selfridge with factored part 50.00%
2^1667321-2^833661+1 is prime! (56794.4485s+0.0014s)
[Elapsed time: 15.78 hours]
modified2011-01-18 10:15:29
created2011-01-14 01:08:01

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