2981 · 21023323 + 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:2981 · 21023323 + 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):L2826 : Jeudy, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:308055   (log10 is 308054.39261483)
Rank (*):14567 (digit rank is 1)
Entrance Rank (*):1820
Currently on list? (*):no
Submitted:10/11/2012 07:56:40 CDT
Last modified:10/11/2012 11:20:24 CDT
Removed (*):9/24/2013 22:09:39 CDT
Database id:109778
Status Flags:none
Score (*):43.0168 (normalized score 0.3553)

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_id109778
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 2981 2 1023323 1 2>&1
[Elapsed time: 10.145 seconds]
modified2012-11-04 23:29:01
created2012-10-11 08:06:13
id149204

fieldvalue
prime_id109778
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"2981*2^1023323+1" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing 2981*2^1023323+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
2981*2^1023323+1 is prime! (2408.4419s+0.0008s)
[Elapsed time: 40.13 minutes]
modified2012-11-04 23:29:01
created2012-10-11 10:37:04
id149218

Query times: 0.0004 seconds to select prime, 0.0008 seconds to seek comments.