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:||137403865536 + 1|
|Verification status (*):||Proven|
|Official Comment:||Generalized Fermat|
|Proof-code(s): (*):||GF3 : Penrose, GFNSieve, GFNSearch, Proth.exe|
|Decimal Digits:||402260 (log10 is 402259.88566142)|
|Rank (*):||4861 (digit rank is 1)|
|Entrance Rank (*):||12|
|Currently on list? (*):||yes|
|Submitted:||5/28/2003 15:44:34 CDT|
|Last modified:||5/28/2003 15:44:34 CDT|
|Score (*):||43.8368 (normalized score 1.0244)|
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 512
Subcategory: "Generalized Fermat"
(archival tag id 204713, tag last modified 2018-02-22 10:50:26)
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||PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor')|
Running N-1 test using base 3
Primality testing 1374038^65536+1 [N-1, Brillhart-Lehmer-Selfridge]
Calling Brillhart-Lehmer-Selfridge with factored part 95.10%
1374038^65536+1 is prime! (-831.537808 seconds)
Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.