6503 · 2635713 + 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:6503 · 2635713 + 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):L2125 : Greer, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:191373   (log10 is 191372.49474729)
Rank (*):25999 (digit rank is 1)
Entrance Rank (*):4642
Currently on list? (*):no
Submitted:2/11/2011 18:00:00 CDT
Last modified:2/11/2011 20:50:24 CDT
Removed (*):2/22/2011 14:57:45 CDT
Database id:98258
Status Flags:none
Score (*):41.5526 (normalized score 0.11)

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_id98258
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 6503 2 635713 1 2>&1
[Elapsed time: 9.714 seconds]
modified2011-12-27 16:48:34
created2011-02-11 18:05:12
id125867

fieldvalue
prime_id98258
person_id9
machineRedHat Virtual STEM Server
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"6503*2^635713+1" 2>&1
PFGW Version 3.3.4.20100405.x86_Stable [GWNUM 25.14]
Primality testing 6503*2^635713+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
6503*2^635713+1 is prime! (595.5433s+0.0011s)
[Elapsed time: 10.08 minutes]
modified2011-03-25 10:27:30
created2011-02-11 20:14:22
id125895

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.