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6 · Bern(5462)/(724389557 · 8572589 · 3742097186099)
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:
|Description:||6 · Bern(5462)/(724389557 · 8572589 · 3742097186099)|
|Verification status (*):||PRP|
|Official Comment (*):||Irregular, ECPP|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||c64 : Metcalfe, Minovic, Ritschel, TOPS, Primo|
|Decimal Digits:||13657 (log10 is 13656.620815761)|
|Rank (*):||76438 (digit rank is 1)|
|Entrance Rank (*):||59565|
|Currently on list? (*):||short|
|Submitted:||5/14/2013 05:18:03 UTC|
|Last modified:||3/11/2023 15:54:10 UTC|
|Score (*):||33.4056 (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.
- Irregular Primes (archivable *)
- Prime on list: yes, rank 7
Subcategory: "Irregular Primes"
(archival tag id 217151, tag last modified 2023-03-11 16:02:31)
- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 164
(archival tag id 217152, 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 114142 person_id 9 machine RedHat P4 P4 what prp notes PFGW Version 184.108.40.206BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 4176531494...8889381213 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N-1 test using base 3 Running N+1 test using discriminant 11, base 3+sqrt(11) Calling N-1 BLS with factored part 0.09% and helper 0.06% (0.33% proof) 4176531494...8889381213 is Fermat and Lucas PRP! (104.7961s+0.0050s) [Elapsed time: 1.73 minutes] modified 2020-07-07 22:30:19 created 2013-05-14 05:23:24 id 158660
field value prime_id 114142 person_id 9 machine Ditto P4 P4 what trial_divided notes PFGW Version 220.127.116.11BIT.20110215.x86_Dev [GWNUM 26.5] 4176531494031264....7529128889381213 1/1 mro=0 trial factoring to 4023025 4176531494...8889381213 has no small factor. [Elapsed time: 21.963 seconds] modified 2020-07-07 22:30:19 created 2013-05-14 05:35:24 id 158662
Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
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