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:||4371219865536 + 1|
|Verification status (*):||Proven|
|Official Comment:||Generalized Fermat|
|Proof-code(s): (*):||L4584 : Goforth, GFNSvCUDA, GeneFer, AthGFNSieve, PrimeGrid, LLR|
|Decimal Digits:||500735 (log10 is 500734.5349337)|
|Rank (*):||2470 (digit rank is 1)|
|Entrance Rank (*):||2206|
|Currently on list? (*):||yes|
|Submitted:||11/4/2018 04:00:56 CDT|
|Last modified:||11/4/2018 05:50:10 CDT|
|Score (*):||44.5096 (normalized score 1.7013)|
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 363
Subcategory: "Generalized Fermat"
(archival tag id 219943, tag last modified 2019-03-23 11:50:17)
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||Using: Xeon 4c+4c 3.5GHz|
|notes||Command: /home/caldwell/client/pfgw/pfgw64 -t -q"43712198^65536+1" 2>&1|
PFGW Version 184.108.40.206BIT.20130722.x86_Dev [GWNUM 27.11]
Primality testing 43712198^65536+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 48.34%
43712198^65536+1 is prime! (5788.2276s+0.0154s)
[Elapsed time: 1.61 hours]
Query times: 0.0006 seconds to select prime, 0.0006 seconds to seek comments.