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167 · 2315872 - 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 · 2315872 - 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L171 : Metcalfe, ProthSieve, Rieselprime, LLR
Decimal Digits:95090   (log10 is 95089.1695068443)
Rank (*):45626 (digit rank is 1)
Entrance Rank (*):2342
Currently on list? (*):no
Submitted:4/8/2006 02:48:21 CDT
Last modified:7/7/2006 07:54:43 CDT
Removed (*):6/7/2007 23:46:56 CDT
Database id:77534
Status Flags:none
Score (*):39.3991 (normalized score 0.0083)

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_id77534
person_id9
machineWinXP P4 2.2GHz
whatprime
notesCommand: pfgw.exe -n -f -tp -q"167*2^315872-1" 2>&1
PFGW Version 1.2.0 for Windows [FFT v23.8]
Primality testing 167*2^315872-1 [N+1, Brillhart-Lehmer-Selfridge]
trial factoring to 32302804
Running N+1 test using discriminant 3, base 1+sqrt(3)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
167*2^315872-1 is prime! (4009.3660s+0.0321s)
[Elapsed time: 4010 seconds]
modified2006-07-14 06:27:06
created2006-04-08 11:39:52
id84047

fieldvalue
prime_id77534
person_id9
machineGenToo P3 400MHz
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 167 2 315872 -1 2>&1
[Elapsed time: 9.226 seconds]
modified2006-07-14 06:27:03
created2006-07-07 07:54:34
id85018

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