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167 · 2275680 - 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 · 2275680 - 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L171 : Metcalfe, ProthSieve, Rieselprime, LLR
Decimal Digits:82991   (log10 is 82990.1719211174)
Rank (*):46815 (digit rank is 1)
Entrance Rank (*):3201
Currently on list? (*):no
Submitted:3/29/2006 11:55:34 CDT
Last modified:3/29/2006 21:28:49 CDT
Removed (*):3/14/2007 14:05:34 CDT
Database id:77437
Status Flags:none
Score (*):38.9797 (normalized score 0.0054)

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_id77437
person_id9
machineGenToo P3 400MHz
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 167 2 275680 -1 2>&1
[Elapsed time: 56.024 seconds]
modified2006-03-31 16:07:06
created2006-03-29 12:23:12
id83880

fieldvalue
prime_id77437
person_id9
machineWinXP P4 2.2GHz
whatprime
notesCommand: pfgw.exe -n -f -tp -q"167*2^275680-1" 2>&1
PFGW Version 1.2.0 for Windows [FFT v23.8]
Primality testing 167*2^275680-1 [N+1, Brillhart-Lehmer-Selfridge]
trial factoring to 27930009
Running N+1 test using discriminant 3, base 1+sqrt(3)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
167*2^275680-1 is prime! (2549.2787s+0.0339s)
[Elapsed time: 2549 seconds]
modified2006-03-31 16:07:05
created2006-03-29 20:46:07
id83901

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