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:||346195465536 + 1|
|Verification status (*):||Proven|
|Official Comment:||Generalized Fermat|
|Proof-code(s): (*):||p316 : Yama, GeneFer, AthGFNSieve, PrimeGrid, OpenPFGW|
|Decimal Digits:||428561 (log10 is 428560.96025669)|
|Rank (*):||5206 (digit rank is 1)|
|Entrance Rank (*):||1238|
|Currently on list? (*):||no|
|Submitted:||1/25/2014 21:25:54 CDT|
|Last modified:||1/26/2014 05:50:54 CDT|
|Removed (*):||9/6/2019 17:53:52 CDT|
|Score (*):||44.0314 (normalized score 0.9685)|
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 937
Subcategory: "Generalized Fermat"
(archival tag id 217590, tag last modified 2019-11-18 07:50:11)
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/pfgw -t -q"3461954^65536+1" 2>&1|
PFGW Version 18.104.22.168BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing 3461954^65536+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 54.99%
3461954^65536+1 is prime! (27749.5296s+0.0295s)
[Elapsed time: 7.71 hours]
Query times: 0.0001 seconds to select prime, 0.0002 seconds to seek comments.