2216091 - 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:2216091 - 1
Verification status (*):Proven
Official Comment:Mersenne 31
Proof-code(s): (*):S : Slowinski
Decimal Digits:65050   (log10 is 65049.8727930254)
Rank (*):46021 (digit rank is 1)
Entrance Rank (*):1
Currently on list? (*):short
Submitted:9/6/1985
Last modified:9/6/1985
Database id:392
Status Flags:none
Score (*):38.2287 (normalized score 0.004)

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.
Mersenne (archivable *)
Prime on list: yes, rank 19
Subcategory: "Mersenne"
(archival tag id 188757, tag last modified 2016-01-19 07:57:44)

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_id392
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -tp -q"2^216091-1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 2^216091-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(28672,20) to FFT(28672,19)
Reduced from FFT(28672,19) to FFT(28672,18)
Reduced from FFT(28672,18) to FFT(28672,17)
Reduced from FFT(28672,17) to FFT(28672,16)
432198 bit request FFT size=(28672,16)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
2^216091-1 is prime! (621.0900s+0.0000s)
[Elapsed time: 10.37 minutes]
modified2008-09-12 14:12:35
created2008-08-05 21:03:43
id100211

Query times: 0.0004 seconds to select prime, 0.0002 seconds to seek comments.