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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 (*):||Euler irregular, ECPP|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||c8 : Broadhurst, Water, Primo|
|Decimal Digits:||3682 (log10 is 3681.226989923)|
|Rank (*):||91984 (digit rank is 2)|
|Entrance Rank (*):||73128|
|Currently on list? (*):||short|
|Submitted:||2/16/2013 18:13:36 UTC|
|Last modified:||3/11/2023 15:54:10 UTC|
|Blob database id:||296|
|Score (*):||29.3373 (normalized score 0)|
Description: (from blob table id=296)
[This prime has a pre-calculated decimal expansion (linked blob)]
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 12
Subcategory: "Euler Irregular primes"
(archival tag id 215087, tag last modified 2023-03-11 15:53:59)
- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 643
(archival tag id 215088, tag last modified 2023-03-11 16:02:30)
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 111260 person_id 9 machine RedHat P4 P4 what trial_divided notes PFGW Version 18.104.22.168BIT.20110215.x86_Dev [GWNUM 26.5] 1686513892468376....9459544889014799 1/1 mro=0 trial factoring to 972159 1686513892...4889014799 has no small factor. [Elapsed time: 1.632 seconds] modified 2020-07-07 22:30:22 created 2013-02-16 18:18:05 id 152793
field value prime_id 111260 person_id 9 machine RedHat P4 P4 what prp notes PFGW Version 22.214.171.124BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 1686513892...4889014799 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 17, base 1+sqrt(17) Calling N-1 BLS with factored part 0.38% and helper 0.13% (1.30% proof) 1686513892...4889014799 is Fermat and Lucas PRP! (6.9821s+0.0022s) [Elapsed time: 7.00 seconds] modified 2020-07-07 22:30:22 created 2013-02-16 18:20:10 id 152795
Query times: 0.0003 seconds to select prime, 0.0007 seconds to seek comments.
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