43721667145 · 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: | 43721667145 · 2371# + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Arithmetic progression (1,d=6658678529*2371#) |
| Proof-code(s): (*): | p308 : DavisK, Underwood, NewPGen, PrimeForm_egroup, OpenPFGW |
| Decimal Digits: | 1014 (log10 is 1013.3908794075) |
| Rank (*): | 130324 (digit rank is 2845) |
| Entrance Rank (*): | 104988 |
| Currently on list? (*): | no |
| Submitted: | 4/11/2013 19:25:43 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 112491 |
| Status Flags: | none |
| Score (*): | 25.3136 (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.
- Arithmetic Progressions of Primes (archivable class *)
- Prime on list: no, rank 1338
Subcategory: "Arithmetic progression (1,d=*)"
(archival tag id 215768, tag last modified 2023-07-02 12:37:19)
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 112491 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/TrialDiv/TrialDiv -q 43721667145 2371 # 1 2>&1 [Elapsed time: 143.839 seconds] modified 2020-07-07 22:30:21 created 2013-04-11 19:26:44 id 155329
field value prime_id 112491 person_id 9 machine Ditto P4 P4 what prime notes Command: /home/ditto/client/pfgw -t -q"43721667145*2371#+1" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 43721667145*2371#+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 33.36% 43721667145*2371#+1 is prime! (0.5978s+0.0006s) [Elapsed time: 1.00 seconds] modified 2020-07-07 22:30:21 created 2013-04-11 19:38:02 id 155334
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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