8051 · 21369811 + 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:8051 · 21369811 + 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):L3035 : Scalise, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:412359   (log10 is 412358.1052403)
Rank (*):3933 (digit rank is 1)
Entrance Rank (*):2239
Currently on list? (*):yes
Submitted:12/13/2015 06:30:01 CDT
Last modified:12/13/2015 07:20:10 CDT
Database id:120747
Status Flags:TrialDiv
Score (*):43.913 (normalized score 1.1765)

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_id120747
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"8051*2^1369811+1" 2>&1
PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11]
Primality testing 8051*2^1369811+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%


8051*2^1369811+1 is prime! (925.7986s+0.0006s)
[Elapsed time: 15.43 minutes]
modified2016-04-08 12:40:27
created2015-12-13 07:02:46
id166377

Query times: 0.0005 seconds to select prime, 0.0006 seconds to seek comments.