271 · 21165420 + 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:271 · 21165420 + 1
Verification status (*):Proven
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L2593 : Johnson6, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:350829   (log10 is 350828.81051601)
Rank (*):13338 (digit rank is 1)
Entrance Rank (*):657
Currently on list? (*):no
Submitted:12/2/2011 21:46:44 CDT
Last modified:12/4/2011 17:28:49 CDT
Removed (*):8/7/2014 09:28:27 CDT
Database id:103440
Status Flags:none
Score (*):43.4164 (normalized score 0.4445)

User comments about this prime (disclaimer):

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Michel Johnson writes (11 Sep 2014):  (report abuse)
Divides xGF(1165419,7,3)

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_id103440
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 271 2 1165420 1 2>&1 [Elapsed time: 10.098 seconds]
modified2020-07-07 17:30:30
created2011-12-02 21:48:01
id136461

fieldvalue
prime_id103440
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"271*2^1165420+1" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 271*2^1165420+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 271*2^1165420+1 is prime! (2763.2309s+0.0010s) [Elapsed time: 46.05 minutes]
modified2020-07-07 17:30:30
created2011-12-02 21:53:01
id136466

Query times: 0.0006 seconds to select prime, 0.0008 seconds to seek comments.
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