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 (*):||Euler irregular, ECPP|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||c77 : Batalov, Primo|
|Decimal Digits:||21257 (log10 is 21256.010012513)|
|Rank (*):||69544 (digit rank is 1)|
|Entrance Rank (*):||66650|
|Currently on list? (*):||short|
|Submitted:||12/26/2020 21:28:24 CDT|
|Last modified:||12/26/2020 21:50:12 CDT|
|Status Flags:||Verify, TrialDiv|
|Score (*):||34.7746 (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.
- Euler Irregular primes (archivable *)
- Prime on list: yes, rank 2
Subcategory: "Euler Irregular primes"
(archival tag id 225770, tag last modified 2022-08-26 14:30:32)
- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 55
(archival tag id 225771, tag last modified 2022-11-14 11:36:29)
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.
field value prime_id 131505 person_id 9 machine Using: Xeon (pool) 4c+4c 3.5GHz what prp notes PFGW Version 22.214.171.124BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 1023322475...3721298279 [N-1/N+1, Brillhart-Lehmer-Selfridge] 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 0.09% and helper 0.03% (0.31% proof) 1023322475...3721298279 is Fermat and Lucas PRP! (35.2613s+0.0026s) [Elapsed time: 36.00 seconds] modified 2021-04-20 17:39:25 created 2020-12-26 21:31:15 id 177200