8289 · 21309405 + 1
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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:8289 · 21309405 + 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):L3035 : Scalise, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:394175   (log10 is 394174.09997453)
Rank (*):4760 (digit rank is 1)
Entrance Rank (*):2349
Currently on list? (*):yes
Submitted:2/14/2015 16:34:04 CDT
Last modified:2/14/2015 17:20:28 CDT
Database id:119325
Status Flags:TrialDiv
Score (*):43.7744 (normalized score 1.0401)

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_id119325
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"8289*2^1309405+1" 2>&1
PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11]
Primality testing 8289*2^1309405+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%


8289*2^1309405+1 is prime! (654.5546s+0.0003s)
[Elapsed time: 10.90 minutes]
modified2015-04-20 07:32:09
created2015-02-14 16:46:26
id164931

Query times: 0.0004 seconds to select prime, 0.0005 seconds to seek comments.