21515 · 48688484017560 · 133579779967573 · 383159376767784 · 960310896529769 + 3
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: | 21515 · 48688484017560 · 133579779967573 · 383159376767784 · 960310896529769 + 3 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Sophie Germain (2p+1) |
| Proof-code(s): (*): | p360 : Kinne, Exoo, OpenPFGW |
| Decimal Digits: | 31112 (log10 is 31111.912792563) |
| Rank (*): | 68013 (digit rank is 1) |
| Entrance Rank (*): | 51101 |
| Currently on list? (*): | no |
| Submitted: | 10/21/2013 22:45:12 UTC |
| Last modified: | 5/20/2023 20:59:19 UTC |
| Database id: | 116056 |
| Status Flags: | none |
| Score (*): | 35.9522 (normalized score 0.0001) |
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.
- Sophie Germain (2p+1) (archivable *)
- Prime on list: no, rank 40
Subcategory: "Sophie Germain (2p+1)"
(archival tag id 217341, tag last modified 2023-11-19 12:37:21)
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 116056 person_id 9 machine RedHat Virtual STEM Server what prime notes PFGW Version 3.3.4.20100405.x86_Stable [GWNUM 25.14] Primality testing 2^1515*48688484017^560*133579779967^573*383159376767^784*960310896529^769+3 [N-1/N+1, Brillhart-Lehmer-Selfridge] Reading factors from helper file helper Running N-1 test using base 2 Running N-1 test using base 5 Running N+1 test using discriminant 11, base 1+sqrt(11) Calling N-1 BLS with factored part 100.00% and helper 0.03% (300.03% proof) 2^1515*48688484017^560*133579779967^573*383159376767^784*960310896529^769+3 is prime! (278.5632s+0.0055s) [Elapsed time: 4.63 minutes] Helper File: 2^1514*48688484017^560*133579779967^573*383159376767^784*960310896529^769+1 modified 2020-07-07 22:30:18 created 2013-10-21 22:46:11 id 161559
Query times: 0.0004 seconds to select prime, 0.0004 seconds to seek comments.
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