13 · 216828072 + 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:13 · 216828072 + 1
Verification status (*):Proven
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):A2 : Propper, Srsieve, PRST
Decimal Digits:5065756   (log10 is 5065755.5551365)
Rank (*):40 (digit rank is 1)
Entrance Rank (*):37
Currently on list? (*):short
Submitted:10/11/2023 19:22:02 UTC
Last modified:10/13/2023 05:37:17 UTC
Database id:136522
Status Flags:none
Score (*):51.6055 (normalized score 717.5258)

User comments about this prime (disclaimer):

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Gary B. Gostin writes (13 Oct 2023):  (report abuse)
Divides xGF(16828066,8,5), xGF(16828068,11,10), xGF(16828070,9,5), xGF(16828070,9,8), xGF(16828071,7,2)

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.
machineUsing: Digital Ocean Droplet
notesCommand: /var/www/clientpool/1/pfgw64 -V -f -t -q"13*2^16828072+1" >command_output 2>&1
PFGW Version [GWNUM 30.11]
Primality testing 13*2^16828072+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 3
Special modular reduction using all-complex AVX-512 FFT length 960K, Pass1=960, Pass2=1K, clm=2 on 13*2^16828072+1
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%

13*2^16828072+1 is prime! (120939.9027s+0.0069s)
[Elapsed time: 33.59 hours]
modified2023-10-13 04:58:42
created2023-10-11 19:23:01

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