21203793 - 2601897 + 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:21203793 - 2601897 + 1
Verification status (*):Proven
Official Comment:Gaussian Mersenne norm 37
Proof-code(s): (*):L192 : Jaworski, LLR
Decimal Digits:362378   (log10 is 362377.80157033)
Rank (*):10318 (digit rank is 1)
Entrance Rank (*):98
Currently on list? (*):short
Submitted:9/20/2006 20:03:49 CDT
Last modified:1/15/2011 08:45:22 CDT
Database id:78531
Status Flags:none
Score (*):43.516 (normalized score 0.7086)

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 187093, 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"2^1203793-2^601897+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
trial factoring to 134377248
2^1203793-2^601897+1 has no small factor.
[Elapsed time: 3281.263 seconds]
modified2007-03-03 21:00:43
created2006-09-20 20:22:01

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -t -q"2^1203793-2^601897+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 2^1203793-2^601897+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(163840,20) to FFT(163840,19)
Reduced from FFT(163840,19) to FFT(163840,18)
Reduced from FFT(163840,18) to FFT(163840,17)
Reduced from FFT(163840,17) to FFT(163840,16)
2407594 bit request FFT size=(163840,16)
Calling Brillhart-Lehmer-Selfridge with factored part 50.00%
2^1203793-2^601897+1 is prime! (-363.8238s+0.0000s)
[Elapsed time: 27998 seconds]
modified2007-03-03 21:00:43
created2006-09-20 20:23:03

Query times: 0.0005 seconds to select prime, 0.0007 seconds to seek comments.