83 · 22342345 + 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:83 · 22342345 + 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):L2626 : DeKlerk, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:705119   (log10 is 705118.02427164)
Rank (*):716 (digit rank is 1)
Entrance Rank (*):134
Currently on list? (*):short
Submitted:4/3/2013 18:07:17 CDT
Last modified:4/3/2013 21:50:25 CDT
Database id:112299
Status Flags:none
Score (*):45.5607 (normalized score 6.1732)

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_id112299
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -t -q"83*2^2342345+1" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing 83*2^2342345+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
83*2^2342345+1 is prime! (12454.3505s+0.0017s)
[Elapsed time: 3.46 hours]
modified2013-04-08 09:17:46
created2013-04-03 18:08:01
id154946

fieldvalue
prime_id112299
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 83 2 2342345 1 2>&1
[Elapsed time: 10.816 seconds]
modified2013-04-08 09:17:46
created2013-04-03 18:18:01
id154947

Query times: 0.0004 seconds to select prime, 0.0011 seconds to seek comments.