89396295016384 + 1
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: | 89396295016384 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Cunningham chain 2nd kind (p), generalized Fermat |
| Proof-code(s): (*): | p427 : Niegocki, GeneFer, AthGFNSieve, PrivGfnServer, OpenPFGW |
| Decimal Digits: | 146659 (log10 is 146658.41901531) |
| Rank (*): | 42462 (digit rank is 2) |
| Entrance Rank (*): | 39098 |
| Currently on list? (*): | short |
| Submitted: | 2/9/2023 10:46:36 UTC |
| Last modified: | 5/20/2023 20:59:19 UTC |
| Database id: | 135153 |
| Status Flags: | none |
| Score (*): | 40.7336 (normalized score 0.0125) |
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.
- Generalized Fermat (archivable *)
- Prime on list: no, rank 4723
Subcategory: "Generalized Fermat"
(archival tag id 228331, tag last modified 2024-10-29 10:37:19)- Cunningham Chains (2nd kind) (archivable class *)
- Prime on list: yes, rank 2, weight 28.003740933819
Subcategory: "Cunningham chain 2nd kind (p)"
(archival tag id 228332, tag last modified 2023-03-17 06:37:21)
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 135153 person_id 9 machine Using: Dual Intel Xeon Gold 5222 CPUs 3.8GHz what prime notes Command: /home/caldwell/clientpool/1/pfgw64 -t -q"893962950^16384+1" 2>&1
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing 893962950^16384+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Calling Brillhart-Lehmer-Selfridge with factored part 42.76%
893962950^16384+1 is prime! (153.9297s+0.0009s)
[Elapsed time: 2.57 minutes]modified 2023-02-09 10:49:36 created 2023-02-09 10:47:01 id 180933
Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.
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