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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:||11029 (log10 is 11028.826856375)|
|Rank (*):||79886 (digit rank is 1)|
|Entrance Rank (*):||67198|
|Currently on list? (*):||short|
|Submitted:||10/25/2014 06:06:51 UTC|
|Last modified:||3/11/2023 15:54:10 UTC|
|Status Flags:||Verify, TrialDiv|
|Score (*):||32.7436 (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 245
(archival tag id 217843, tag last modified 2023-03-11 16:02:30)
- Lucas cofactor (archivable *)
- Prime on list: yes, rank 8
Subcategory: "Lucas cofactor"
(archival tag id 217844, 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 118671 person_id 9 machine Using: Xeon 4c+4c 3.5GHz what prp notes Command: /home/caldwell/client/pfgw/pfgw64 -tc -q"V(52859)/1124137922466041911" 2>&1 PFGW Version 220.127.116.11BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing V(52859)/1124137922466041911 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Running N-1 test using base 13 Running N+1 test using discriminant 43, base 1+sqrt(43) Calling N-1 BLS with factored part 0.17% and helper 0.01% (0.53% proof) V(52859)/1124137922466041911 is Fermat and Lucas PRP! (10.9351s+0.0024s) [Elapsed time: 11.00 seconds] modified 2020-07-07 22:30:17 created 2014-10-25 06:11:01 id 164253
Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.
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