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:||9812766262144 + 1|
|Verification status (*):||Proven|
|Official Comment:||Generalized Fermat|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||L4245 : Greer, GFNSvCUDA, GeneFer, AthGFNSieve, PrimeGrid, LLR|
|Decimal Digits:||1832857 (log10 is 1832856.17592114)|
|Rank (*):||108 (digit rank is 1)|
|Entrance Rank (*):||87|
|Currently on list? (*):||short|
|Submitted:||2/16/2020 02:56:46 CDT|
|Last modified:||2/17/2020 03:20:25 CDT|
|Score (*):||48.4911 (normalized score 74.2511)|
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: yes, rank 19
Subcategory: "Generalized Fermat"
(archival tag id 223823, tag last modified 2020-06-04 13:20:26)
User comments about this prime (disclaimer):
User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.
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"9812766^262144+1" 2>&1|
PFGW Version 126.96.36.199BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing 9812766^262144+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Calling Brillhart-Lehmer-Selfridge with factored part 36.15%
9812766^262144+1 is prime! (87048.3165s+0.0626s)
[Elapsed time: 24.18 hours]
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.