The hardware and software on this system was updated September 4th.
Please let me know of any problem you encounter.
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:
|Description:||82659189 · 226997 + 1|
|Verification status (*):||Proven|
|Official Comment:||Cunningham chain 2nd kind (p)|
|Proof-code(s): (*):||L983 : Wu_T, LLR|
|Decimal Digits:||8135 (log10 is 8134.8240840805)|
|Rank (*):||69758 (digit rank is 1)|
|Entrance Rank (*):||47392|
|Currently on list? (*):||no|
|Submitted:||3/22/2010 00:13:26 CDT|
|Last modified:||3/22/2010 00:50:47 CDT|
|Score (*):||31.8 (normalized score 0)|
There are certain forms classed as
archivable: these prime may (at times)
remain on this list even if they do not make
the Top 5000 proper. Such primes are tracked with archival
- Cunningham Chains (2nd kind) (archivable class *)
- Prime on list: no, rank 21, weight 21.9621302067784
Subcategory: "Cunningham chain 2nd kind (p)"
(archival tag id 212440, tag last modified 2014-07-18 20:21:43)
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.
|machine||RedHat P4 P4|
|notes||Command: /home/caldwell/client/TrialDiv/TrialDiv -q 82659189 2 26997 1 2>&1|
[Elapsed time: 8.184 seconds]
|machine||Ditto P4 P4|
|notes||Command: /home/ditto/client/pfgw -t -q"82659189*2^26997+1" 2>&1|
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 82659189*2^26997+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(3584,21) to FFT(3584,20)
Reduced from FFT(3584,20) to FFT(3584,19)
Reduced from FFT(3584,19) to FFT(3584,18)
Reduced from FFT(3584,18) to FFT(3584,17)
Reduced from FFT(3584,17) to FFT(3584,16)
54056 bit request FFT size=(3584,16)
Calling Brillhart-Lehmer-Selfridge with factored part 99.90%
82659189*2^26997+1 is prime! (3.5800s+0.0000s)
[Elapsed time: 4.00 seconds]
Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.