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:||7 · 2804534 + 1|
|Verification status (*):||Proven|
|Official Comment:||Divides GF(804533,12)|
|Proof-code(s): (*):||g196 : Odermatt, Proth.exe|
|Decimal Digits:||242190 (log10 is 242189.711629565)|
|Rank (*):||18154 (digit rank is 1)|
|Entrance Rank (*):||51|
|Currently on list? (*):||short|
|Submitted:||12/10/2003 12:40:47 CDT|
|Last modified:||12/10/2003 12:40:47 CDT|
|Score (*):||42.2771 (normalized score 0.2098)|
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
- Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
- Prime on list: yes, rank 19, weight 44.2230384122281
Subcategory: "Divides GF(*,12)"
(archival tag id 187121, tag last modified 2016-03-15 13:57:15)
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"7*2^804534+1" 2>&1|
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 7*2^804534+1 [N-1, Brillhart-Lehmer-Selfridge]
trial factoring to 87539581
Running N-1 test using base 3
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)
1609082 bit request FFT size=(98304,17)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
7*2^804534+1 is prime! (10832.8091s+0.0006s)
Query times: 0.0003 seconds to select prime, 0.0003 seconds to seek comments.