2683143625525 · 235176 + 13
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.
|Description:||2683143625525 · 235176 + 13|
|Verification status (*):||PRP|
|Official Comment (*):||Consecutive primes arithmetic progression (3,d=6),ECPP|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||c92 : Lamprecht, Luhn, Primo|
|Decimal Digits:||10602 (log10 is 10601.459771397)|
|Rank (*):||78413 (digit rank is 2)|
|Entrance Rank (*):||74668|
|Currently on list? (*):||short|
|Submitted:||12/30/2019 22:23:49 CDT|
|Last modified:||12/30/2019 22:50:24 CDT|
|Status Flags:||Verify, TrialDiv|
|Score (*):||32.6211 (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.
- Consecutive Primes in Arithmetic Progression (archivable class *)
- Prime on list: yes, rank 4
Subcategory: "Consecutive primes in arithmetic progression (3,d=*)"
(archival tag id 223656, tag last modified 2022-04-16 01:37:19)
- Arithmetic Progressions of Primes (archivable class *)
- Prime on list: no, rank 133, weight 38.226747322138
Subcategory: "Arithmetic progression (3,d=*)"
(archival tag id 223657, tag last modified 2022-05-27 13:58:11)
- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 216
(archival tag id 223658, tag last modified 2022-06-26 16:37:20)
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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 130217 person_id 9 machine Using: Xeon 4c+4c 3.5GHz what prp notes Command: /home/caldwell/client/pfgw/pfgw64 -tc -q"2683143625525*2^35176+13" 2>&1 PFGW Version 22.214.171.124BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 2683143625525*2^35176+13 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 5, base 4+sqrt(5) Calling N-1 BLS with factored part 0.14% and helper 0.01% (0.43% proof) 2683143625525*2^35176+13 is Fermat and Lucas PRP! (2.7766s+0.0001s) [Elapsed time: 3.00 seconds] modified 2020-07-07 17:30:10 created 2019-12-30 22:31:05 id 175903