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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 cofactor, ECPP|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||c77 : Batalov, Primo|
|Decimal Digits:||16159 (log10 is 16158.699227345)|
|Rank (*):||74090 (digit rank is 1)|
|Entrance Rank (*):||69528|
|Currently on list? (*):||short|
|Submitted:||8/23/2020 09:25:59 UTC|
|Last modified:||3/11/2023 15:54:10 UTC|
|Status Flags:||Verify, TrialDiv|
|Score (*):||33.9264 (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.
- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 122
(archival tag id 225644, tag last modified 2023-03-11 16:02:30)
- Lucas cofactor (archivable *)
- Prime on list: yes, rank 5
Subcategory: "Lucas cofactor"
(archival tag id 225645, tag last modified 2023-03-11 15:53:59)
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 131080 person_id 9 machine Using: Xeon (pool) 4c+4c 3.5GHz what prp notes Command: /home/caldwell/clientpool/1/pfgw64 -tc -q"V(77417)/313991497376559420151" 2>&1 PFGW Version 220.127.116.11BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing V(77417)/3139914973...6559420151 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N-1 test using base 13 Running N+1 test using discriminant 19, base 1+sqrt(19) Calling N-1 BLS with factored part 0.09% and helper 0.03% (0.32% proof) V(77417)/3139914973...6559420151 is Fermat and Lucas PRP! (22.3625s+0.0057s) [Elapsed time: 23.00 seconds] modified 2021-04-20 22:39:26 created 2020-08-23 09:26:01 id 176768
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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