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:||27 · 2672007 + 1|
|Verification status (*):||Proven|
|Official Comment:||Divides Fermat F(672005)|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||g279 : Cooper, NewPGen, PRP, Proth.exe|
|Decimal Digits:||202296 (log10 is 202295.695659929)|
|Rank (*):||21729 (digit rank is 1)|
|Entrance Rank (*):||192|
|Currently on list? (*):||short|
|Submitted:||8/29/2005 21:54:48 CDT|
|Last modified:||8/30/2005 07:33:25 CDT|
|Score (*):||41.7234 (normalized score 0.1308)|
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
- Fermat Divisors (archivable *)
- Prime on list: yes, rank 15, weight 45.0192959029823
Subcategory: "Divides Fermat"
(archival tag id 187210, tag last modified 2016-03-15 13:57:14)
User comments about this prime (disclaimer):
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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||Linux P4 2.8GHz|
|notes||Command: /home/caldwell/client/pfgw -f -t -q"27*2^672007+1" 2>&1|
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 27*2^672007+1 [N-1, Brillhart-Lehmer-Selfridge]
trial factoring to 72273173
Running N-1 test using base 5
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(98304,20) to FFT(98304,19)
Reduced from FFT(98304,19) to FFT(98304,18)
Reduced from FFT(98304,18) to FFT(98304,17)
Reduced from FFT(98304,17) to FFT(98304,16)
1344032 bit request FFT size=(98304,16)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
27*2^672007+1 is prime! (9915.2392s+0.0506s)
[Elapsed time: 9916 seconds]
Query times: 0.0002 seconds to select prime, 0.0001 seconds to seek comments.