418059269664 · 2371# + 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: | 418059269664 · 2371# + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Cunningham chain 2nd kind (16p-15) |
| Proof-code(s): (*): | p308 : DavisK, Underwood, NewPGen, PrimeForm_egroup, OpenPFGW |
| Decimal Digits: | 1015 (log10 is 1014.3714205514) |
| Rank (*): | 128067 (digit rank is 33) |
| Entrance Rank (*): | 92253 |
| Currently on list? (*): | no |
| Submitted: | 4/18/2011 01:24:00 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 99745 |
| Status Flags: | none |
| Score (*): | 25.3166 (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.
- Cunningham Chains (2nd kind) (archivable class *)
- Prime on list: no, rank 11, weight 45.575990997424
Subcategory: "Cunningham chain 2nd kind (16p-15)"
(archival tag id 213207, tag last modified 2023-03-11 15:53:59)
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 99745 person_id 9 machine RedHat Virtual STEM Server what prime notes Command: /home/caldwell/client/pfgw -t -q"418059269664*2371#+1" 2>&1 PFGW Version 3.3.4.20100405.x86_Stable [GWNUM 25.14] Primality testing 418059269664*2371#+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2377 Calling Brillhart-Lehmer-Selfridge with factored part 33.45% 418059269664*2371#+1 is prime! (0.1474s+0.0002s) [Elapsed time: 1.00 seconds] modified 2020-07-07 22:30:31 created 2011-04-18 01:25:24 id 129012
field value prime_id 99745 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/TrialDiv/TrialDiv -q 418059269664 2371 # 1 2>&1 [Elapsed time: 143.394 seconds] modified 2020-07-07 22:30:31 created 2011-04-18 01:44:36 id 129017
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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