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167 · 2314000 - 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.

Description:167 · 2314000 - 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L171 : Metcalfe, ProthSieve, Rieselprime, LLR
Decimal Digits:94526   (log10 is 94525.6413549612)
Rank (*):45672 (digit rank is 1)
Entrance Rank (*):2372
Currently on list? (*):no
Submitted:4/7/2006 11:23:44 CDT
Last modified:7/7/2006 07:55:44 CDT
Removed (*):6/4/2007 20:31:23 CDT
Database id:77529
Status Flags:none
Score (*):39.3808 (normalized score 0.0081)

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_id77529
person_id9
machineGenToo P3 400MHz
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 167 2 314000 -1 2>&1
[Elapsed time: 9.272 seconds]
modified2006-07-14 06:27:03
created2006-07-07 07:55:35
id85024

fieldvalue
prime_id77529
person_id9
machineWinXP Pent_M 1.7GHz Laptop
whatprime
notesCommand: pfgw.exe -n -tp -q"167*2^314000-1" 2>&1
PFGW Version 20030811.Win_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Running N+1 test using discriminant 3, base 1+sqrt(3)
N+1: 167*2^314000Primality testing 167*2^314000-1 [N+1, Brillhart-Lehmer-Selfridge]
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
167*2^314000-1 is prime! (2956.1952s+0.0010s)
-1[Elapsed time: 2956 seconds]
modified2006-04-07 19:06:05
created2006-04-07 18:08:35
id84041

Query times: 0.0004 seconds to select prime, 0.0003 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.