2991961 - 2495981 + 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.

This prime's information:

Description:2991961 - 2495981 + 1
Verification status (*):Proven
Official Comment (*):Gaussian Mersenne norm 36, generalized unique
Proof-code(s): (*):x28 : Iskra
Decimal Digits:298611   (log10 is 298610.01552884)
Rank (*):23308 (digit rank is 1)
Entrance Rank (*):108
Currently on list? (*):short
Submitted:11/29/2005 09:21:01 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:76312
Status Flags:none
Score (*):42.921 (normalized score 0.1149)

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 6
Subcategory: "Gaussian Mersenne norm"
(archival tag id 187105, tag last modified 2023-03-11 15:53:59)
Generalized Unique (archivable *)
Prime on list: no, rank 138
Subcategory: "Generalized Unique"
(archival tag id 224202, tag last modified 2023-12-18 15:37:22)

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]
modified2020-07-07 22:30:43
created2005-11-29 09:23:00
id81518

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