2 · 31086112 + 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:2 · 31086112 + 1
Verification status (*):Proven
Official Comment:
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p199 : Broadhurst, NewPGen, OpenPFGW
Decimal Digits:518208   (log10 is 518207.42123608)
Rank (*):2649 (digit rank is 1)
Entrance Rank (*):91
Currently on list? (*):yes
Submitted:2/13/2010 17:00:24 CDT
Last modified:2/14/2010 09:20:21 CDT
Database id:91751
Status Flags:none
Score (*):44.6149 (normalized score 1.6087)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

David Broadhurst writes (11 Sep 2014): 
Until February 2010, we knew of no prime that contains more than a million zeros when written in a base b > 2. Then, on successive days, two were discovered. This one is the larger.

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.
machineDitto P4 P4
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 2 3 1086112 1 2>&1
[Elapsed time: 9.533 seconds]
modified2011-12-27 16:48:40
created2010-02-13 17:05:01

machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -t -q"2*3^1086112+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 2*3^1086112+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(229376,19) to FFT(229376,18)
Reduced from FFT(229376,18) to FFT(229376,17)
Reduced from FFT(229376,17) to FFT(229376,16)
3442904 bit request FFT size=(229376,16)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
2*3^1086112+1 is prime! (56982.9327s+0.1376s)
[Elapsed time: 15.83 hours]
modified2010-03-13 18:56:30
created2010-02-13 17:22:12

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.