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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|
|Proof-code(s): (*):||c8 : Broadhurst, Water, Primo|
|Decimal Digits:||8295 (log10 is 8294.9708491467)|
|Rank (*):||82574 (digit rank is 1)|
|Entrance Rank (*):||67430|
|Currently on list? (*):||short|
|Submitted:||11/7/2013 16:50:17 UTC|
|Last modified:||3/11/2023 15:54:10 UTC|
|Status Flags:||Verify, TrialDiv|
|Score (*):||31.8605 (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 346
(archival tag id 217428, tag last modified 2023-03-11 16:02:30)
- Lucas cofactor (archivable *)
- Prime on list: yes, rank 17
Subcategory: "Lucas cofactor"
(archival tag id 217429, tag last modified 2023-03-11 15:53:59)
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 116239 person_id 9 machine Ditto P4 P4 what prp notes Command: /home/ditto/client/pfgw -tc -q"V(39769)/18139109172816581" 2>&1 PFGW Version 22.214.171.124BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing V(39769)/18139109172816581 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 11, base 1+sqrt(11) Calling N-1 BLS with factored part 0.13% and helper 0.01% (0.41% proof) V(39769)/18139109172816581 is Fermat and Lucas PRP! (27.4723s+0.0036s) [Elapsed time: 27.00 seconds] modified 2020-07-07 22:30:18 created 2013-11-07 18:13:49 id 161742
Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
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