49568 · 5640900 - 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:49568 · 5640900 - 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):p321 : Dinkel, Srsieve, PrimeGrid, SierpinskiRiesel, OpenPFGW
Decimal Digits:447975   (log10 is 447974.57098035)
Rank (*):3655 (digit rank is 1)
Entrance Rank (*):188
Currently on list? (*):yes
Submitted:7/1/2011 22:58:12 CDT
Last modified:7/2/2011 09:50:21 CDT
Database id:100681
Status Flags:none
Score (*):44.1676 (normalized score 1.2327)

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_id100681
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 49568 5 640900 -1 2>&1
[Elapsed time: 9.974 seconds]
modified2011-12-27 16:48:31
created2011-07-01 23:05:01
id130927

fieldvalue
prime_id100681
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -tp -q"49568*5^640900-1" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing 49568*5^640900-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
49568*5^640900-1 is prime! (37074.8457s+0.0329s)
[Elapsed time: 10.30 hours]
modified2011-12-27 16:48:31
created2011-07-01 23:08:02
id130928

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