8229 · 2695527 + 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.

This prime's information:

Description:8229 · 2695527 + 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L2681 : Buzko, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:209379   (log10 is 209378.40514124)
Rank (*):30211 (digit rank is 1)
Entrance Rank (*):3507
Currently on list? (*):no
Submitted:9/13/2011 05:49:29 UTC
Last modified:3/11/2023 15:54:10 UTC
Removed (*):2/7/2012 18:30:56 UTC
Database id:101956
Status Flags:none
Score (*):41.8293 (normalized score 0.0433)

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_id101956
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 8229 2 695527 1 2>&1 [Elapsed time: 10.097 seconds]
modified2020-07-07 22:30:30
created2011-09-13 05:52:02
id133478

fieldvalue
prime_id101956
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"8229*2^695527+1" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 8229*2^695527+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 8229*2^695527+1 is prime! (1368.4311s+0.0006s) [Elapsed time: 22.82 minutes]
modified2020-07-07 22:30:30
created2011-09-13 05:53:01
id133480

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