28993093368077 · 2399# + 19421
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: | 28993093368077 · 2399# + 19421 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Sextuplet (2), ECPP |
| Proof-code(s): (*): | c18 : Luhn, Primo |
| Decimal Digits: | 1037 (log10 is 1036.4795789638) |
| Rank (*): | 127208 (digit rank is 35) |
| Entrance Rank (*): | 110142 |
| Currently on list? (*): | yes |
| Submitted: | 3/14/2016 07:19:20 UTC |
| Last modified: | 11/20/2024 23:37:22 UTC |
| Database id: | 121425 |
| Status Flags: | none |
| Score (*): | 25.3841 (normalized score 0) |
Archival tags:
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.
- Sextuplet (archivable class *)
- Prime on list: yes, rank 1
Subcategory: "Sextuplet (2)"
(archival tag id 229753, tag last modified 2024-11-20 23:37:24)- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 1175
Subcategory: "ECPP"
(archival tag id 229752, tag last modified 2024-11-20 23:37:23)
Verification data:
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 121425 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -tc -hhelper.php?id=1100000000828520308 -q"28993093368077*2399#+19421" 2>&1
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing 28993093368077*2399#+19421 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000000828520308
Running N-1 test using base 2
Running N+1 test using discriminant 17, base 1+sqrt(17)
Running N+1 test using discriminant 17, base 2+sqrt(17)
Calling N+1 BLS with factored part 100.00% and helper 2.73% (302.73% proof)
28993093368077*2399#+19421 is prime! (0.4282s+0.0002s)
[Elapsed time: 1.00 seconds]
Helper File:
2
5
971
73897
206511583
181467182081
3
13
83
17923916861296524864522043554637524...(1032 digits)...04596272845232283396299863925718783modified 2023-03-13 07:42:35 created 2023-03-13 07:42:34 id 181570
field value prime_id 121425 person_id 9 machine Using: Xeon 4c+4c 3.5GHz what prp notes Command: /home/caldwell/client/pfgw/pfgw64 -tc -q"28993093368077*2399#+19421" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 28993093368077*2399#+19421 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 17, base 1+sqrt(17) Calling N-1 BLS with factored part 0.84% and helper 0.49% (3.05% proof) 28993093368077*2399#+19421 is Fermat and Lucas PRP! (0.2540s+0.0004s) [Elapsed time: 1.00 seconds] modified 2020-07-07 22:30:16 created 2016-03-14 07:21:01 id 167056
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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