21667321 - 2833661 + 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.

Description:21667321 - 2833661 + 1
Verification status (*):Proven
Official Comment (*):Gaussian Mersenne norm 38?, generalized unique
Proof-code(s): (*):L137 : Jaworski, Rieselprime, LLR
Decimal Digits:501914   (log10 is 501913.63340047)
Rank (*):3423 (digit rank is 1)
Entrance Rank (*):109
Currently on list? (*):short
Submitted:1/14/2011 01:06:44 CDT
Last modified:8/4/2020 13:21:48 CDT
Database id:97416
Status Flags:none
Score (*):44.5168 (normalized score 1.3748)

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 4
Subcategory: "Gaussian Mersenne norm"
(archival tag id 213060, tag last modified 2020-08-02 20:20:04)
Generalized Unique (archivable *)
Prime on list: no, rank 70
Subcategory: "Generalized Unique"
(archival tag id 224146, tag last modified 2020-08-04 13:50:04)

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_id97416
person_id9
machineDitto P4 P4
whatprime
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]
modified2020-07-07 17:30:32
created2011-01-14 01:08:01
id124221

fieldvalue
prime_id97416
person_id9
machineRedHat P4 P4
whattrial_divided
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]
modified2020-07-07 17:30:32
created2011-01-14 01:18:02
id124222

Query times: 0.0007 seconds to select prime, 0.0002 seconds to seek comments.
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