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 (*):||Fibonacci number, ECPP|
|Proof-code(s): (*):||x48 : Asuncion, Allombert, Unknown|
|Decimal Digits:||27173 (log10 is 27172.43248794)|
|Rank (*):||67369 (digit rank is 1)|
|Entrance Rank (*):||65021|
|Currently on list? (*):||short|
|Submitted:||5/4/2021 09:54:52 CDT|
|Last modified:||5/4/2021 10:20:35 CDT|
|Status Flags:||Verify, TrialDiv|
|Score (*):||35.5338 (normalized score 0.0001)|
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.
- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 26
(archival tag id 226106, tag last modified 2022-10-15 20:37:20)
- Fibonacci Number (archivable *)
- Prime on list: yes, rank 2
Subcategory: "Fibonacci Number"
(archival tag id 226107, tag last modified 2021-09-18 09:37:41)
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 132290 person_id 9 machine Using: Xeon (pool) 4c+4c 3.5GHz what prp notes Command: /home/caldwell/clientpool/1/pfgw64 -tc -q"U(130021)" 2>&1 PFGW Version 184.108.40.206BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing U(130021) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N-1 test using base 7 Running N+1 test using discriminant 13, base 1+sqrt(13) Calling N-1 BLS with factored part 0.52% and helper 0.23% (1.79% proof) U(130021) is Fermat and Lucas PRP! (71.9279s+0.1439s) [Elapsed time: 72.00 seconds] modified 2021-05-14 12:47:21 created 2021-05-04 09:56:01 id 178002