The nth Prime Page
will now find any of the first 2,623,557,157,654,233 primes or
) for x
up to 100,000,000,000,000,000.
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:||16869987339975 · 2171960 + 1|
|Verification status (*):||Proven|
|Official Comment:||Twin (p+2)|
|Proof-code(s): (*):||x24 : Jarai_Z, Farkas, Csajbok, Kasza, Jarai, Unknown|
|Decimal Digits:||51779 (log10 is 51778.3451691349)|
|Rank (*):||49078 (digit rank is 1)|
|Entrance Rank (*):||8233|
|Currently on list? (*):||short|
|Submitted:||9/8/2005 03:46:06 CDT|
|Last modified:||9/8/2005 09:38:09 CDT|
|Score (*):||37.5249 (normalized score 0.002)|
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
- Twin Primes (archivable *)
- Prime on list: yes, rank 10
Subcategory: "Twin (p+2)"
(archival tag id 189943, tag last modified 2016-04-02 09:20:06)
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"16869987339975*2^171960+1" 2>&1|
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 16869987339975*2^171960+1 [N-1, Brillhart-Lehmer-Selfridge]
trial factoring to 16857726
Running N-1 test using base 17
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(24576,20) to FFT(24576,19)
Reduced from FFT(24576,19) to FFT(24576,18)
Reduced from FFT(24576,18) to FFT(24576,17)
Reduced from FFT(24576,17) to FFT(24576,16)
344016 bit request FFT size=(24576,16)
Calling Brillhart-Lehmer-Selfridge with factored part 99.98%
16869987339975*2^171960+1 is prime! (879.6136s+0.0004s)
[Elapsed time: 880 seconds]
Query times: 0.0005 seconds to select prime, 0.0006 seconds to seek comments.