55339803 · 219400 + 1
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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

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:55339803 · 219400 + 1
Verification status (*):Proven
Official Comment:Cunningham chain 2nd kind (p)
Proof-code(s): (*):L983 : Wu_T, LLR
Decimal Digits:5848   (log10 is 5847.7249534901)
Rank (*):80707 (digit rank is 1)
Entrance Rank (*):50082
Currently on list? (*):no
Submitted:12/8/2009 07:46:57 CDT
Last modified:12/8/2009 08:06:38 CDT
Database id:91117
Status Flags:none
Score (*):30.7756 (normalized score 0)

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.
Cunningham Chains (2nd kind) (archivable class *)
Prime on list: no, rank 48, weight 21.2677975908484
Subcategory: "Cunningham chain 2nd kind (p)"
(archival tag id 212483, tag last modified 2017-12-20 01:20:25)

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/TrialDiv/TrialDiv -q 55339803 2 19400 1 2>&1
[Elapsed time: 7.570 seconds]
modified2011-12-27 16:48:41
created2009-12-08 07:48:45

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -t -q"55339803*2^19400+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 55339803*2^19400+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(2560,21) to FFT(2560,20)
Reduced from FFT(2560,20) to FFT(2560,19)
Reduced from FFT(2560,19) to FFT(2560,18)
Reduced from FFT(2560,18) to FFT(2560,17)
Reduced from FFT(2560,17) to FFT(2560,16)
38860 bit request FFT size=(2560,16)
Calling Brillhart-Lehmer-Selfridge with factored part 99.87%
55339803*2^19400+1 is prime! (1.9800s+0.0000s)
[Elapsed time: 2.00 seconds]
modified2010-03-13 18:56:32
created2009-12-08 08:06:00

Query times: 0.0009 seconds to select prime, 0.0008 seconds to seek comments.