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:||2 · 43156947 + 1|
|Verification status (*):||Proven|
|Official Comment:||Divides Phi(431^56947,2)|
|Proof-code(s): (*):||g404 : Taniguchi, Proth.exe|
|Decimal Digits:||150026 (log10 is 150025.87813384)|
|Rank (*):||26796 (digit rank is 1)|
|Entrance Rank (*):||1135|
|Currently on list? (*):||no|
|Submitted:||11/13/2007 20:38:43 CDT|
|Last modified:||11/13/2007 21:44:39 CDT|
|Score (*):||40.8035 (normalized score 0.071)|
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
- Divides Phi (archivable *)
- Prime on list: no, rank 29
Subcategory: "Divides Phi"
(archival tag id 187402, tag last modified 2014-08-20 21:21:19)
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 2 431 56947 1 2>&1|
[Elapsed time: 8.229 seconds]
|machine||RedHat P4 P4|
|notes||Command: /home/caldwell/client/pfgw -t -q"2*431^56947+1" 2>&1|
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 2*431^56947+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(65536,20) to FFT(65536,19)
Reduced from FFT(65536,19) to FFT(65536,18)
Reduced from FFT(65536,18) to FFT(65536,17)
Reduced from FFT(65536,17) to FFT(65536,16)
996760 bit request FFT size=(65536,16)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
2*431^56947+1 is prime! (-1256.8673s+0.0300s)
[Elapsed time: 51.63 minutes]
Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.