At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important PrimePages database: 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:
|Verification status (*):||PRP|
|Official Comment (*):||Lucas primitive part, ECPP|
|Proof-code(s): (*):||c74 : Lasher, Dubner, Primo|
|Decimal Digits:||12324 (log10 is 12323.583685745)|
|Rank (*):||78992 (digit rank is 2)|
|Entrance Rank (*):||67102|
|Currently on list? (*):||short|
|Submitted:||7/30/2015 04:50:49 UTC|
|Last modified:||5/20/2023 20:59:19 UTC|
|Score (*):||33.0875 (normalized score 0)|
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 tags.
- Lucas primitive part (archivable *)
- Prime on list: yes, rank 20
Subcategory: "Lucas primitive part"
(archival tag id 218068, tag last modified 2023-03-11 15:53:59)
- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 220
(archival tag id 218069, tag last modified 2023-10-03 00:37:15)
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.
field value prime_id 120167 person_id 9 machine Using: Xeon 4c+4c 3.5GHz what prp notes PFGW Version 126.96.36.199BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 3834296954...8766162001 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 37 Running N-1 test using base 67 Running N+1 test using discriminant 89, base 14+sqrt(89) Calling N-1 BLS with factored part 0.75% and helper 0.00% (2.27% proof) 3834296954...8766162001 is Fermat and Lucas PRP! (12.0999s+0.0039s) [Elapsed time: 12.00 seconds] modified 2020-07-07 22:30:17 created 2015-07-30 04:51:02 id 165795