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:||572186131072 + 1|
|Verification status (*):||Proven|
|Official Comment:||Generalized Fermat|
|Proof-code(s): (*):||g0 : Gallot, Proth.exe|
|Decimal Digits:||754652 (log10 is 754651.919478865)|
|Rank (*):||1202 (digit rank is 1)|
|Entrance Rank (*):||9|
|Currently on list? (*):||short|
|Submitted:||1/8/2004 13:14:59 CDT|
|Last modified:||1/8/2004 13:14:59 CDT|
|Score (*):||45.7691 (normalized score 5.0853)|
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 (archivable *)
- Prime on list: no, rank 291
Subcategory: "Generalized Fermat"
(archival tag id 204698, tag last modified 2020-02-24 19:20:26)
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"572186^131072+1" 2>&1|
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 572186^131072+1 [N-1, Brillhart-Lehmer-Selfridge]
trial factoring to 292713744
Running N-1 test using base 3
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(393216,19) to FFT(393216,18)
Reduced from FFT(393216,18) to FFT(393216,17)
Reduced from FFT(393216,17) to FFT(393216,16)
5013808 bit request FFT size=(393216,16)
Calling Brillhart-Lehmer-Selfridge with factored part 73.40%
572186^131072+1 is prime! (316839.6743s+0.8418s)
Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.