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 · 23511774 + 1|
|Verification status (*):||Proven|
|Official Comment:||Divides GF(3511773,6)|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||p236 : Cooper, NewPGen, PRP, OpenPFGW|
|Decimal Digits:||1057151 (log10 is 1057150.15709092)|
|Rank (*):||270 (digit rank is 1)|
|Entrance Rank (*):||21|
|Currently on list? (*):||short|
|Submitted:||11/14/2008 15:17:50 CDT|
|Last modified:||11/24/2008 21:50:02 CDT|
|Score (*):||46.8035 (normalized score 17.1888)|
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 2, weight 48.7494651442748
Subcategory: "Divides GF(*,6)"
(archival tag id 187014, tag last modified 2016-03-15 13:57:15)
User comments about this prime (disclaimer):
User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.
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 7 2 3511774 1 2>&1|
[Elapsed time: 11.255 seconds]
|machine||RedHat P4 P4|
|notes||Command: /home/caldwell/client/pfgw -t -q"7*2^3511774+1" 2>&1|
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 7*2^3511774+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(458752,19) to FFT(458752,18)
Reduced from FFT(458752,18) to FFT(458752,17)
Reduced from FFT(458752,17) to FFT(458752,16)
7023562 bit request FFT size=(458752,16)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
7*2^3511774+1 is prime! (103531.8685s+0.0026s)
[Elapsed time: 28.76 hours]
Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.