5355 · 2808766 + 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:5355 · 2808766 + 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):L2093 : McNeill, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:243467   (log10 is 243466.55423265)
Rank (*):19475 (digit rank is 1)
Entrance Rank (*):3128
Currently on list? (*):no
Submitted:4/6/2012 06:12:29 CDT
Last modified:4/6/2012 06:50:25 CDT
Removed (*):7/2/2012 06:01:22 CDT
Database id:106096
Status Flags:none
Score (*):42.2933 (normalized score 0.1723)

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_id106096
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 5355 2 808766 1 2>&1
[Elapsed time: 10.281 seconds]
modified2012-07-16 11:33:01
created2012-04-06 06:18:30
id141785

fieldvalue
prime_id106096
person_id9
machineRedHat Virtual STEM Server
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"5355*2^808766+1" 2>&1
PFGW Version 3.3.4.20100405.x86_Stable [GWNUM 25.14]
Primality testing 5355*2^808766+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 19
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
5355*2^808766+1 is prime! (849.5262s+0.0209s)
[Elapsed time: 14.32 minutes]
modified2012-07-16 11:33:01
created2012-04-06 06:34:42
id141787

Query times: 0.0005 seconds to select prime, 0.0006 seconds to seek comments.