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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:||10305 (log10 is 10304.633719775)|
|Rank (*):||80378 (digit rank is 1)|
|Entrance Rank (*):||63613|
|Currently on list? (*):||short|
|Submitted:||6/16/2013 14:48:33 UTC|
|Last modified:||3/11/2023 15:54:10 UTC|
|Score (*):||32.5331 (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 284
(archival tag id 217185, tag last modified 2023-03-11 16:02:30)
- Lucas cofactor (archivable *)
- Prime on list: yes, rank 14
Subcategory: "Lucas cofactor"
(archival tag id 217186, 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 114432 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/pfgw -o -f -q"V(49391)/298414424560419239" 2>&1 PFGW Version 184.108.40.206BIT.20110215.x86_Dev [GWNUM 26.5] V(49391)/298414424560419239 1/1 mro=0 trial factoring to 2968100 V(49391)/298414424560419239 has no small factor. [Elapsed time: 2.761 seconds] modified 2020-07-07 22:30:19 created 2013-06-16 14:52:02 id 159242
field value prime_id 114432 person_id 9 machine RedHat P4 P4 what prp notes Command: /home/caldwell/client/pfgw -tc -q"V(49391)/298414424560419239" 2>&1 PFGW Version 220.127.116.11BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing V(49391)/298414424560419239 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Running N-1 test using base 11 Running N+1 test using discriminant 23, base 1+sqrt(23) Calling N-1 BLS with factored part 0.11% and helper 0.00% (0.35% proof) V(49391)/298414424560419239 is Fermat and Lucas PRP! (53.2562s+0.0042s) [Elapsed time: 53.00 seconds] modified 2020-07-07 22:30:19 created 2013-06-16 14:53:01 id 159243
Query times: 0.0004 seconds to select prime, 0.0005 seconds to seek comments.
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