2719 · 2636678 + 1
(Another of the Prime Pages' resources)
The Largest Known Primes Icon
  View this page in:   language help

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:2719 · 2636678 + 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):L1125 : Laluk, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:191663   (log10 is 191662.60998856)
Rank (*):26941 (digit rank is 1)
Entrance Rank (*):4718
Currently on list? (*):no
Submitted:2/13/2011 09:52:45 CDT
Last modified:2/13/2011 10:20:53 CDT
Removed (*):2/22/2011 20:35:37 CDT
Database id:98372
Status Flags:none
Score (*):41.5573 (normalized score 0.0955)

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.
machineDitto P4 P4
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 2719 2 636678 1 2>&1
[Elapsed time: 9.927 seconds]
modified2011-12-27 16:48:34
created2011-02-13 10:05:02

machineRedHat Virtual STEM Server
notesCommand: /home/caldwell/client/pfgw -t -q"2719*2^636678+1" 2>&1
PFGW Version [GWNUM 25.14]
Primality testing 2719*2^636678+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
2719*2^636678+1 is prime! (598.4043s+0.0010s)
[Elapsed time: 10.03 minutes]
modified2011-03-25 10:27:30
created2011-02-13 10:01:50

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