2991961 - 2495981 + 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:2991961 - 2495981 + 1
Verification status (*):Proven
Official Comment:Gaussian Mersenne norm 36
Proof-code(s): (*):x28 : Iskra
Decimal Digits:298611   (log10 is 298610.015528838)
Rank (*):13259 (digit rank is 1)
Entrance Rank (*):108
Currently on list? (*):short
Submitted:11/29/2005 03:21:01 CDT
Last modified:6/18/2006 17:21:39 CDT
Database id:76312
Status Flags:none
Score (*):42.921 (normalized score 0.4334)

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 5
Subcategory: "Gaussian Mersenne norm"
(archival tag id 187105, 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.
fieldvalue
prime_id76312
person_id9
machineLinux P4 2.8GHz
whatprime
notesCommand: /home/caldwell/client/pfgw -f -t -q"2^991961-2^495981+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 2^991961-2^495981+1 [N-1, Brillhart-Lehmer-Selfridge]
trial factoring to 109386855
Running N-1 test using base 13
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(131072,20) to FFT(131072,19)
Reduced from FFT(131072,19) to FFT(131072,18)
Reduced from FFT(131072,18) to FFT(131072,17)
Reduced from FFT(131072,17) to FFT(131072,16)
1983930 bit request FFT size=(131072,16)
Calling Brillhart-Lehmer-Selfridge with factored part 50.00%
2^991961-2^495981+1 is prime! (19609.3144s+0.0092s)
[Elapsed time: 19609 seconds]
modified2005-12-10 11:09:15
created2005-11-29 03:23:00
id81518

Query times: 0.0005 seconds to select prime, 0.0004 seconds to seek comments.