8397 · 2623186 + 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:8397 · 2623186 + 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L1935 : Channing, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:187602   (log10 is 187601.60300201)
Rank (*):34437 (digit rank is 1)
Entrance Rank (*):4891
Currently on list? (*):no
Submitted:2/10/2011 03:09:44 UTC
Last modified:3/11/2023 15:54:10 UTC
Removed (*):2/11/2011 19:11:09 UTC
Database id:98112
Status Flags:none
Score (*):41.4914 (normalized score 0.0362)

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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 8397 2 623186 1 2>&1 [Elapsed time: 9.793 seconds]
modified2020-07-07 22:30:32
created2011-02-10 03:18:32

machineRedHat Virtual STEM Server
notesCommand: /home/caldwell/client/pfgw -t -q"8397*2^623186+1" 2>&1 PFGW Version [GWNUM 25.14] Primality testing 8397*2^623186+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 8397*2^623186+1 is prime! (582.0520s+0.0097s) [Elapsed time: 9.88 minutes]
modified2020-07-07 22:30:32
created2011-02-10 03:31:35

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