3431 · 2734133 + 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:3431 · 2734133 + 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):L1957 : Hemsley, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:221000   (log10 is 220999.5892275)
Rank (*):21431 (digit rank is 1)
Entrance Rank (*):3199
Currently on list? (*):no
Submitted:12/8/2011 14:52:23 CDT
Last modified:12/8/2011 15:50:24 CDT
Removed (*):3/29/2012 10:15:14 CDT
Database id:103531
Status Flags:none
Score (*):41.9955 (normalized score 0.1294)

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_id103531
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 3431 2 734133 1 2>&1
[Elapsed time: 10.120 seconds]
modified2011-12-27 16:48:25
created2011-12-08 15:05:02
id136651

fieldvalue
prime_id103531
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -t -q"3431*2^734133+1" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing 3431*2^734133+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
3431*2^734133+1 is prime! (1428.8336s+0.0008s)
[Elapsed time: 23.82 minutes]
modified2011-12-27 16:48:25
created2011-12-08 15:08:01
id136661

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