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6853 · 2840306 + 1

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important PrimePages database: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.

Description:6853 · 2840306 + 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L1204 : Brown1, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:252962   (log10 is 252961.14741715)
Rank (*):19551 (digit rank is 1)
Entrance Rank (*):2747
Currently on list? (*):no
Submitted:4/23/2012 18:40:07 CDT
Last modified:4/23/2012 19:20:26 CDT
Removed (*):8/28/2012 11:08:32 CDT
Database id:106517
Status Flags:none
Score (*):42.4109 (normalized score 0.1685)

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_id106517
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 6853 2 840306 1 2>&1
[Elapsed time: 9.655 seconds]
modified2012-07-16 11:33:00
created2012-04-23 18:48:01
id142622

fieldvalue
prime_id106517
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"6853*2^840306+1" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing 6853*2^840306+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
6853*2^840306+1 is prime! (1608.5132s+0.0009s)
[Elapsed time: 26.80 minutes]
modified2012-07-16 11:33:00
created2012-04-23 18:53:01
id142624

Query times: 0.0009 seconds to select prime, 0.0006 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.