196597 · 22178109 - 1
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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:196597 · 22178109 - 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):L175 : Duggan, ProthSieve, RieselSieve, LLR
Decimal Digits:655682   (log10 is 655681.436402565)
Rank (*):1071 (digit rank is 1)
Entrance Rank (*):21
Currently on list? (*):short
Submitted:5/9/2006 06:01:07 CDT
Last modified:7/7/2006 00:52:23 CDT
Database id:77753
Status Flags:none
Score (*):45.3375 (normalized score 4.3477)

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.
machineWinXP P4 2.2GHz M
notesCommand: pfgw.exe -n -f -tp -q"196597*2^2178109-1" 2>&1
PFGW Version 1.2.0 for Windows [FFT v23.8]
Primality testing 196597*2^2178109-1 [N+1, Brillhart-Lehmer-Selfridge]
trial factoring to 252181701
Running N+1 test using discriminant 3, base 1+sqrt(3)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
196597*2^2178109-1 is prime! (264634.1630s+0.0938s)
[Elapsed time: 264618 seconds]
modified2006-07-14 06:27:05
created2006-05-10 11:28:00

machineGenToo P3 400MHz
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 196597 2 2178109 -1 2>&1
[Elapsed time: 10.116 seconds]
modified2006-07-14 06:27:04
created2006-07-07 00:52:12

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.